CN111144020A - Method, device, computer device and storage medium for membrane-based system buckling simulation - Google Patents
Method, device, computer device and storage medium for membrane-based system buckling simulation Download PDFInfo
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Abstract
The invention discloses a method, equipment, computer equipment and a storage medium for simulating film-based system buckling, wherein the method comprises the steps of obtaining initial acceleration according to an initial characteristic matrix and initial displacement of a film, obtaining an integral constant according to a time step, obtaining an equivalent stiffness matrix at the time t according to the initial stiffness characteristic matrix and the integral constant, obtaining an equivalent force vector at the time t according to the initial equivalent force characteristic matrix, initial speed, the integral constant and initial acceleration, obtaining a displacement increment at the time t of the film according to the equivalent stiffness matrix at the time t and the equivalent force vector at the time t, obtaining displacement at the time t according to the initial displacement and the displacement increment at the time t, obtaining acceleration at the time t and speed at the time t according to the displacement increment at the time t, the initial speed and the initial acceleration, and solving the problem that the deviation of a theoretical value of a flexible electronic device caused by applying a Green strain tensor to calculate is larger than the actual situation, the accuracy of the theoretical numerical calculation of the flexible electronic device is improved.
Description
Technical Field
The present application relates to the field of thin film technology, and in particular, to a method, apparatus, computer apparatus, and storage medium for film-based system buckling simulation.
Background
The structure composed of the rigid film and the flexible substrate is referred to as a film-based system for short, fig. 1 is a schematic diagram of the state change of the film-based system in the related art, and under the action of critical load, the surface of the system can be changed from a plane surface in an initial state to a wave-shaped surface in a pre-strain release state and an external force bearing state, and the phenomenon is called buckling instability which is the most important failure mode of the film-based system. Bowden et al utilize the buckling instability of the membrane-based system to control the buckling behavior of the membrane, and realize a good periodic configuration of the rigid membrane on the flexible substrate, wherein the structural dimension range of the periodic configuration can be changed between 100nm and 100 μm, i.e., the patterning under the micro-nano scale is realized by a controllable buckling method. The innovative work of Bowden et al offers more possibilities for the application of film-based systems, of which Flexible Electronic Technology (FET for short) is one of the most important applications, and the ductility of Electronic components can be achieved by innovative structural design using conventional high-performance inorganic semiconductor materials, such as silicon.
In the related art, due to the particularity of the flexible electronic device, the deformation of the flexible electronic device often has strong geometric non-linear characteristics such as large displacement, large rotation, large strain and the like, and the von K rm strain or Green strain tensor is adopted in the prior art to calculate the geometric non-linear deformation. Although the Green strain tensor overcomes the defect that the Cauchy strain tensor generates false strain when a deformable body rotates purely, the Green strain tensor limits the application of the calculation method in the problems of large displacement and large rotation, and serious deviation occurs between the theoretical numerical analysis result of the flexible electronic device at the beginning of design and the actual situation.
Aiming at the problem that the deviation between the theoretical numerical value and the actual condition of the flexible electronic device is large due to the fact that the Green strain tensor is used for calculation in the related technology, an effective solution is not provided at present.
Disclosure of Invention
Aiming at the problem that the deviation between the theoretical numerical value and the actual condition of a flexible electronic device is large due to the fact that the Green strain tensor is used for calculation in the related technology, the invention provides a method, equipment, computer equipment and a storage medium for film-based system buckling simulation, and at least solves the problem.
According to one aspect of the present invention, there is provided a method of membrane-based system buckling simulation, the method comprising:
acquiring the initial speed, the initial characteristic matrix and the initial displacement of the thin film buckling, acquiring the initial acceleration according to the initial characteristic matrix and the initial displacement, and acquiring an integral constant according to the time step length of the thin film buckling;
obtaining an equivalent stiffness matrix at the time t according to the initial stiffness characteristic matrix and the integral constant, and obtaining an equivalent force vector at the time t according to the initial equivalent force characteristic matrix, the initial speed, the integral constant and the initial acceleration;
and obtaining the displacement increment of the film at the t moment according to the equivalent stiffness matrix at the t moment and the equivalent force vector at the t moment, obtaining the displacement at the t moment according to the initial displacement and the displacement increment at the t moment, obtaining the acceleration at the t moment according to the displacement increment at the t moment, the initial speed and the initial acceleration, and obtaining the speed at the t moment according to the initial speed, the initial acceleration and the acceleration at the t moment.
In one embodiment, after obtaining the displacement at the time t, obtaining the acceleration at the time t, and obtaining the velocity at the time t, the method further includes:
obtaining displacement at the t + △ t moment, acceleration at the t + △ t moment and speed at the t + △ t moment according to the time step, the displacement at the t moment, the acceleration at the t moment and the speed at the t moment, wherein △ t is the time step;
stopping the simulation of the membrane-based system buckling in the event that the time step accumulates for a period of time greater than a preset period of time.
In one embodiment, the obtaining the displacement at the time t + △ t, the acceleration at the time t + △ t and the speed at the time t + △ t according to the time step, the displacement at the time t, the acceleration at the time t and the speed at the time t includes:
approximating the displacement increment of the t moment and the speed of the t moment according to a moving least square MLS difference shape function to obtain an approximate displacement increment and an approximate speed, wherein the boundary condition of the MLS difference shape function is an increment variational equation;
and obtaining approximate displacement according to the approximate displacement increment, and obtaining displacement at the t + △ t moment, acceleration at the t + △ t moment and speed at the t + △ t moment according to the time step, the approximate displacement, the acceleration at the t moment and the approximate speed.
In one embodiment, the boundary condition of the MLS difference shape function is an incremental variational equation including:
the increment variational equation is obtained according to a penalty function method.
In one embodiment, before the acquiring the initial velocity, the initial feature matrix, and the initial displacement of the thin film buckling, the method comprises:
under the condition that the uniaxial buckling mode of the film is a cosine curve, acquiring axial displacement and deflection of the film in a towing coordinate system, wherein the deflection is obtained according to the amplitude and wave number of the buckling of the film;
and acquiring a strain tensor of the thin film according to the axial displacement and an average rotation angle of the buckling of the thin film, and acquiring a rotation tensor of the thin film through the average rotation angle, wherein the average rotation angle is obtained by a second component of the axial displacement in the towing coordinate system.
In one embodiment, said obtaining the deflection of said film comprises:
obtaining the bending energy of the thin film according to the amplitude, the wavelength of the thin film buckling and the geometric characteristics;
obtaining the film energy of the film according to the in-plane strain of the film and the geometrical characteristics, wherein the in-plane strain is obtained according to the strain tensor and the pre-applied strain;
and obtaining the amplitude and the wavelength according to the bending energy and the film energy, and obtaining the deflection according to the amplitude and the wavelength.
According to another aspect of the invention, there is provided a membrane-based system buckling simulation apparatus comprising an initial module, an equivalent module, and a dynamics calculation module:
the initial module is used for acquiring the initial speed, the initial characteristic matrix and the initial displacement of the thin film buckling, acquiring the initial acceleration according to the initial characteristic matrix and the initial displacement, and acquiring the integral constant according to the time step length of the thin film buckling;
the equivalent module is used for obtaining an equivalent stiffness matrix at the time t according to an initial stiffness characteristic matrix and the integral constant, and obtaining an equivalent force vector at the time t according to an initial equivalent force characteristic matrix, the initial speed, the integral constant and the initial acceleration;
the dynamics calculation module is used for obtaining the displacement increment of the film at the t moment according to the equivalent stiffness matrix at the t moment and the equivalent force vector at the t moment, obtaining the displacement at the t moment according to the initial displacement and the displacement increment at the t moment, obtaining the acceleration at the t moment according to the displacement increment at the t moment, the initial speed and the initial acceleration, and obtaining the speed at the t moment according to the initial speed, the initial acceleration and the acceleration at the t moment.
In one embodiment, the apparatus further comprises a cycle module and a stop module:
the circulation module is used for obtaining displacement at the t + △ t moment, acceleration at the t + △ t moment and speed at the t + △ t moment according to the time step, the displacement at the t moment, the acceleration at the t moment and the speed at the t moment, wherein △ t is the time step;
the stopping module is used for stopping the simulation of the buckling of the membrane-based system when the accumulated time period of the time step is greater than a preset time period.
According to another aspect of the present invention, there is provided a computer device comprising a memory storing a computer program and a processor implementing any of the methods described above when the processor executes the computer program.
According to another aspect of the invention, there is provided a computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements any of the methods described above.
By the method, the initial speed, the initial characteristic matrix and the initial displacement of the thin film buckling are obtained, the initial acceleration is obtained according to the initial characteristic matrix and the initial displacement, the integral constant is obtained according to the time step of the thin film buckling, the equivalent stiffness matrix at the time t is obtained according to the initial stiffness characteristic matrix and the integral constant, the equivalent force vector at the time t is obtained according to the initial equivalent force characteristic matrix, the initial speed, the integral constant and the initial acceleration, the displacement increment at the time t of the thin film is obtained according to the equivalent stiffness matrix at the time t and the equivalent force vector at the time t, the displacement increment at the time t is obtained according to the initial displacement and the displacement increment at the time t, the acceleration at the time t is obtained according to the displacement increment at the time t, the initial speed and the acceleration at the time t, and the speed at the time t is obtained according to, the problem that the deviation between the theoretical numerical value of the flexible electronic device and the actual condition is large due to the fact that the Green strain tensor is used for calculation is solved, and the accuracy of the calculation of the theoretical numerical value of the flexible electronic device is improved.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the invention without limiting the invention to a proper form.
In the drawings:
FIG. 1 is a schematic view showing a state change of a thin film according to the related art;
FIG. 2 is a schematic representation of an application environment for a method of membrane-based system buckling simulation according to an embodiment of the present invention;
FIG. 3 is a first flowchart of a method of membrane-based system buckling simulation according to an embodiment of the present disclosure;
FIG. 4 is a flow chart two of a method of membrane-based system buckling simulation according to an embodiment of the present invention;
FIG. 5 is a flow chart three of a method of membrane-based system buckling simulation according to an embodiment of the present invention;
FIG. 6 is a schematic diagram of a tow coordinate system according to an embodiment of the invention;
FIG. 7 is a first flowchart of modeling membrane-based system buckling simulation according to an embodiment of the present invention;
FIG. 8 is a second flowchart of the modeling of membrane-based system buckling simulation according to an embodiment of the present invention;
FIG. 9 is a block diagram I of the configuration of a membrane-based system buckling simulation apparatus according to an embodiment of the present invention;
FIG. 10 is a block diagram II of the apparatus for membrane-based system buckling simulation according to an embodiment of the present invention;
FIG. 11 is a schematic structural view of a membrane according to an embodiment of the invention;
FIG. 12 is a schematic illustration of a post-buckling mode of a membrane according to an embodiment of the invention;
FIG. 13 is a schematic illustration of a copper foil post-buckling analysis according to an embodiment of the present invention;
FIG. 14 is a schematic illustration of a thin film transient analysis according to an embodiment of the invention;
fig. 15 is a schematic diagram of the internal structure of a computer device according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.
The method for simulating buckling of a membrane-based system provided by the present application can be applied to the application environment shown in fig. 2, where fig. 2 is a schematic application environment diagram of the method for simulating buckling of a membrane-based system according to an embodiment of the present invention, and as shown in fig. 2, a terminal 202 communicates with a server 204 through a network. The method includes the steps that a user inputs an initial characteristic matrix, initial displacement, initial speed and time step length of a film at a terminal 202, a server 204 obtains initial acceleration according to the initial characteristic matrix and the initial displacement, an integral constant is obtained according to the time step length of buckling of the film, the server 204 obtains an equivalent stiffness matrix at the t moment according to the initial stiffness characteristic matrix and the integral constant, an equivalent force vector at the t moment is obtained according to the initial equivalent force characteristic matrix, the initial speed, the integral constant and the initial acceleration, a displacement increment at the t moment of the film is obtained according to the equivalent stiffness matrix at the t moment and the equivalent force vector at the t moment by the server 204, a first displacement is obtained according to the initial displacement and the displacement increment at the t moment, and a first acceleration and a first speed are obtained through a Newmark method. The terminal 202 may be, but not limited to, various personal computers, notebook computers, smart phones, tablet computers, and portable wearable devices, the server 204 may be implemented by an independent server or a server cluster formed by a plurality of servers, and the terminal 202 and the server 204 may be the same.
In one embodiment, a method for membrane-based system buckling simulation is provided, and fig. 3 is a flow chart one of a method for membrane-based system buckling simulation according to an embodiment of the present invention, as shown in fig. 3, the method comprising the steps of:
step S302, acquiring an initial speed, an initial characteristic matrix and an initial displacement of the film buckling, acquiring an initial acceleration according to the initial characteristic matrix and the initial displacement, and acquiring an integral constant according to the time step of the film buckling. The initial characteristic matrix comprises an initial stiffness matrix, an initial mass matrix and a load vector, wherein the initial stiffness matrix, the initial mass matrix and the load vector are respectively calculated according to the elastic modulus, the density and the external load condition of the structure, and the parameters are determined under the condition that the material and the external condition are determined. In order to ensure successful simulation of the film buckling, an initial defect needs to be given to the film model in the initial stage of model building, in the embodiment, an initial half-cycle sinusoidal deformation is given to the film structure, and the amplitude is generally 0.01 to 0.1 times the thickness of the film. The initial acceleration a can be obtained from the following equation 1:
A＝M-1(F-K·u0) Equation 1
Wherein K is an initial stiffness matrix, M is an initial mass matrix, F is a load vector, u0Is the initial displacement. The integration constant can be obtained from the following equation 2:
wherein A is1、A2、A3、A4、A5For integration constants, △ t is the time step, β and γ are parameters.
And S304, obtaining an equivalent stiffness matrix at the time t according to the initial stiffness characteristic matrix and the integral constant, and obtaining an equivalent force vector at the time t according to the initial equivalent force characteristic matrix, the initial speed, the integral constant and the initial acceleration. Wherein the initial velocity belongs to an initial condition, and in general, the structure is stationary at an initial time, so the initial velocity is generally zero, the initial stiffness feature matrix includes a linear stiffness matrix, a nonlinear stiffness matrix, a penalty function stiffness matrix and an initial mass matrix, and the initial equivalent force feature matrix includes an external force vector, a stress integral vector and a penalty function force vector. the equivalent stiffness matrix at time t can be obtained from the following equation 3:
tKe＝KL-KN+Kα+A1 m formula 3
Wherein the content of the first and second substances,tKeis the equivalent stiffness matrix at time t, KLIs a linear stiffness matrix, KNIs a non-linear stiffness matrix, KαStiffness as a penalty functionThe matrix, M, is an initial quality matrix, t + △ t indicates, in the case of an initial time t, the time at which a time step △ t has elapsed, the equivalent force vector at time t can be obtained from the following equation 4:
tFe＝tR-F+Fα+M(A3V+A4A) equation 4
Wherein the content of the first and second substances,tFeis the first vector of the equivalent power,tr is an external force vector, F is a stress integral vector, KαTo the penalty function force vector, V is the velocity at the initial time and A is the acceleration at the initial time.
Step S306, obtaining a displacement increment of the film at the time t according to the equivalent stiffness matrix at the time t and the equivalent force vector at the time t, obtaining a displacement at the time t according to the initial displacement and the displacement increment at the time t, obtaining an acceleration at the time t according to the displacement increment at the time t, the initial velocity and the initial acceleration, and obtaining a velocity at the time t according to the initial velocity, the initial acceleration and the acceleration at the time t, where the displacement increment at the time t is a deformation increment of the film buckling within a time step △ t, and the displacement increment at the time t can be obtained by the following formula 5:
wherein the content of the first and second substances,tΔ u is the displacement increment at time t. the acceleration at time t and the velocity at time t can be approximately calculated by a Newmark method, and are obtained according to the following formula 6:
after the displacement increment, the speed and the acceleration of the film at the time t are obtained, the dynamic parameters of the film can be analyzed, and the simulation result of the buckling of the film is obtained.
Through the steps S302 to S306, the dynamic parameters in the film buckling process are calculated according to the Newmark method, on the basis of calculating the speed and displacement in the related technology, the acceleration in the film buckling process is further calculated, a more accurate simulation result is obtained, the defects of Green are overcome based on the application of S-R and decomposition theorem, the problem that the deviation between the theoretical numerical value of the flexible electronic device and the actual situation is larger due to the fact that the strain tensor of the Green is used for calculation is solved, and the accuracy of the calculation of the theoretical numerical value of the flexible electronic device is improved.
In one embodiment, fig. 4 is a flow chart two of a method of membrane-based system buckling simulation according to an embodiment of the invention, as shown in fig. 4, the method further comprising the steps of:
and S402, obtaining displacement at the t + △ t moment, acceleration at the t + △ t moment and speed at the t + △ t moment according to the time step, the displacement at the t moment, the acceleration at the t moment and the speed at the t moment, wherein △ t is the time step, wherein since the flexible material is easy to deform greatly, △ t should be a small value as possible, for example, △ t is an initial value which is one thousandth of the total time, and when the calculation result is not converged, the △ t value is continuously reduced until the result is converged.
And step S404, stopping the simulation of the film-based system when the time step is accumulated for a time period greater than a preset time period, wherein the preset time period can be 1S or 2S, for example, the preset time period is 1S, △ t is 0.02S, the time length of the superposition of 50 pieces of △ t is 1S, and when the calculation of the 51 st △ t is carried out, the circulation is stopped, and the result of the film buckling simulation is output.
Through the steps S402 to S404, a small time step △ t is taken for circulation, and the result of the film buckling simulation is obtained through circulation calculation, so that the calculation result is more accurate.
In one embodiment, fig. 5 is a flow chart three of a method for membrane-based system buckling simulation according to an embodiment of the present invention, as shown in fig. 5, the method may further include the steps of:
step S502, the displacement increment of the t moment and the speed of the t moment are approximated according to the moving least square MLS difference function to obtain an approximate displacement increment and an approximate speed, wherein the MLS difference functionThe boundary condition of the number is an increment variational equation, and the MLS difference shape function is one of the methods for forming an approximation function of a mesh-free method. FIG. 6 is a schematic diagram of a tow coordinate system according to an embodiment of the invention, in which
The vector is a vector before deformation, g is a vector after deformation, and an incremental variational equation of a global weak form gridless method is obtained by adopting proper assumption and simplification based on S-R (string-Rotation) and a decomposition theorem, an updated towing coordinate method and a generalized Euler kinematics formula and combining a stress-Strain constitutive relation. Wherein S is a symmetric sub-transformation and represents a strain tensor, R is an orthogonal sub-transformation and represents a rotation tensor, and the incremental variational equation can be obtained by the following formula 7:
wherein, the prime mark "-" indicates that the corresponding physical quantity is the initial towing system at the time t of the towing coordinate system
The following physical quantities;
is an elastic matrix;
and
respectively representing strain rate and rotation rate;t+ΔtWineandt+ΔtWextrespectively inertial force power and external force virtual power.
According to the non-grid Galerkin method, the displacement increment of the node at the time t is increasedtΔukAnd velocitytV, approximated using a Moving Least Squares (MLS) interpolation shape function, where the displacement increment can be obtained from equation 8 as follows:
wherein the content of the first and second substances,tψkas a shape function of the MLS for node k at time t,tΔukis the displacement increment parameter of the node k at the time t. The velocity can be obtained from the following equation 9:
wherein the content of the first and second substances,tv is the velocity parameter of node k at time t.
And step S504, obtaining approximate displacement according to the approximate displacement increment, and obtaining displacement at the t + △ t moment, acceleration at the t + △ t moment and speed at the t + △ t moment according to the time step, the approximate displacement, the acceleration at the t moment and the approximate speed.
Through the steps S502 and S504, based on the energy principle, the virtual power relation among the internal force, the external force and the inertia force at the t + delta t moment is established, based on the S-R and the decomposition theorem and the updated towing coordinate method, the global weak incremental variation equation with the physical quantity at the t moment as the basic quantity is obtained by adopting the speed type physical relation and a proper hypothesis, the incremental variation equation is subjected to discrete processing based on the gridless Galerkin method, the standard format for calculating the film dynamic buckling numerical value is obtained, and the accuracy of the theoretical numerical value calculation of the flexible electronic device is further improved.
In one embodiment, the incremental variational equation is derived according to a penalty function method. Since the MLS sigmoid function approximation does not possess the properties of the Kronecker delta function, the application of the intrinsic boundary conditions can be either a Penalty function Method (Penalty Method) or a Lagrange Multiplier Method (Lagrange Multiplier Method). In the case of the penalty function method, equation 7 is transformed into equation 10 as follows:
the penalty function method is that a constrained optimization problem is converted into a solution unconstrained optimization problem, searching is carried out in a feasible domain, and under the condition that the current solution is far away from a constrained boundary, the penalty function value is very small, otherwise, the penalty function value is close to infinity. And by a penalty function method, the calculation process is simplified, and the calculation efficiency is improved.
In one embodiment, fig. 7 is a flow chart of modeling membrane-based system buckling simulation according to an embodiment of the invention, as shown in fig. 7, the method comprising:
step S702, under the condition that the uniaxial buckling mode of the film is a cosine curve, obtaining the axial displacement and the deflection of the film in a dragging coordinate system, wherein the deflection is obtained according to the amplitude and the wave number of the buckling of the film. When the deflection is stressed or changes in non-uniform temperature, the axis of the object moves linearly in the direction perpendicular to the axis or the middle surface of the plate shell moves linearly in the direction perpendicular to the middle surface, and under the condition that the uniaxial buckling mode of the film is a cosine curve, the deflection can be obtained by the following formula 11 assuming that the axial displacement of the film is a constant:
u2＝A(t)cos(kx1) Equation 11
Wherein u is2Is deflection, x1The coordinate component of the film along the direction 1 in the dragging coordinate system is shown; a (t) is the amplitude of the buckling mode, k is the wave number, the amplitude changes along with the time t, and the wavelength is lambda 2 pi/k, wherein the wavelength is far larger than the thickness h of the filmfThe relationship between the wavelength and the thickness satisfies lambda>>h, or hk<<1。
Step S704, obtaining a strain tensor of the thin film according to the axial displacement and the average rotation angle of the buckling of the thin film, and obtaining a rotation tensor of the thin film according to the average rotation angle, wherein the average rotation angle is obtained from a second component of the axial displacement in the towing coordinate system. For a two-dimensional film subjected to only unidirectional loading, since the film itself is thin, the nonlinear geometric relationship based on S-R and the decomposition theorem can be simplified, wherein the strain tensor can be obtained by the following equation 12:
wherein the content of the first and second substances,
to be the strain tensor, θ is the average rotation angle.
The rotation tensor can be obtained by the following equation 13:
wherein the content of the first and second substances,
for the rotation tensor, the average rotation angle can be obtained by the following equation 14:
wherein u is2|1Is to X2The covariate derivative of (c).
Through the steps S702 and S704, a more accurate nonlinear geometric relationship is adopted to establish a model of the film buckling through S-R and the decomposition theorem, and a new calculation method is provided for the film buckling calculation so as to improve the precision of the film buckling simulation calculation.
In one embodiment, fig. 8 is a second flow chart of modeling membrane-based system buckling simulation according to an embodiment of the invention, as shown in fig. 8, the method further comprising:
step S802, obtaining the bending energy of the film according to the amplitude, the wavelength of the film buckling and the geometric characteristics. Wherein the geometric characteristics include length, area strain modulus, and thickness of the film. The bending energy can be obtained from the following equation 15:
wherein, UbFor bending energy, L0Is the length of the film,
Is the surface strain modulus, h, of the filmfThe thickness of the film, A is the amplitude, and λ is the wavelength.
Step S804, obtaining the film energy of the film according to the in-plane strain of the film and the geometric feature, wherein the in-plane strain is obtained according to the strain tensor and the pre-applied strain. The space-time variation calculation formula of deflection can be obtained through the calculation formulas of axial displacement, deflection, strain tensor and average rotation angle, and is shown in formula 16:
the film energy can be obtained by the following equation 17:
wherein, UmIs the film energy, NmIs the film force, epsilonmIs the in-plane strain. The film force can be obtained by the following equation 18:
wherein in-plane strain εmThis can be obtained from the following equation 19:
wherein epsilonpreIs a pre-applied strain.
Step S806, obtaining the amplitude and the wavelength according to the bending energy and the film energy, and obtaining the deflection according to the amplitude and the wavelength. In the present embodiment, the amplitude a (t) and the wavelength λ are obtained by the minimum energy principle, and the amplitude and the wavelength can be obtained by the following formula 20:
through the steps S802 to S806, a more accurate nonlinear geometric relationship for performing the film buckling simulation is provided, so that the accuracy of the film buckling simulation calculation is further improved.
It should be understood that, although the respective steps in the flowcharts of fig. 3 to 8 are sequentially shown as indicated by arrows, the steps are not necessarily sequentially performed in the order indicated by the arrows. The steps are not performed in the exact order shown and described, and may be performed in other orders, unless explicitly stated otherwise. Moreover, at least some of the steps in fig. 3-8 may include multiple sub-steps or multiple stages that are not necessarily performed at the same time, but may be performed at different times, and the order of performing the sub-steps or stages is not necessarily sequential, but may be performed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.
Corresponding to the above method for simulating membrane-based system buckling, in this embodiment, there is also provided a device for simulating membrane-based system buckling, which is used to implement the above embodiments and preferred embodiments, and which has already been described and will not be described again. As used below, the term "module" may be a combination of software and/or hardware that implements a predetermined function. Although the devices described in the following embodiments are preferably implemented in software, implementations in hardware or a combination of software and hardware are also possible and contemplated.
In one embodiment, a membrane-based system buckling simulation apparatus is provided, and fig. 9 is a block diagram of a structure of the membrane-based system buckling simulation apparatus according to the embodiment of the present invention, as shown in fig. 9, including an initial module 92, an equivalent module 94, and a kinetic calculation module 96, wherein:
the initial module 92 is configured to obtain an initial velocity, an initial feature matrix, and an initial displacement of the film buckling, obtain an initial acceleration according to the initial feature matrix and the initial displacement, and obtain an integral constant according to a time step of the film buckling. In the embodiment, an initial half-cycle sinusoidal deformation is given to the thin film structure, and the amplitude is generally 0.01 to 0.1 times the thickness of the thin film.
And the equivalence module 94 is configured to obtain an equivalent stiffness matrix at the time t according to the initial stiffness feature matrix and the integral constant, and obtain an equivalent force vector at the time t according to the initial equivalent force feature matrix, the initial velocity, the integral constant, and the initial acceleration. The first stiffness feature matrix comprises a linear stiffness matrix, a nonlinear stiffness matrix, a penalty function stiffness matrix and an initial mass matrix, and the first equivalent force feature matrix comprises an external force vector, a stress integral vector and a penalty function force vector.
And the dynamics calculation module 96 is configured to obtain a displacement increment of the film at the time t according to the equivalent stiffness matrix at the time t and the equivalent force vector at the time t, obtain a displacement at the time t according to the initial displacement and the displacement increment at the time t, obtain an acceleration at the time t according to the displacement increment at the time t, the initial velocity and the initial acceleration, and obtain a velocity at the time t according to the initial velocity, the initial acceleration and the acceleration at the time t.
Through the modules 92 to 96, the equivalent module 94 obtains the initial parameters in the initial module 92, and obtains the first equivalent characteristic matrix and the first equivalent vector according to the initial parameters, the dynamics calculation module 96 calculates the dynamics parameters in the film buckling process according to the Newmark method, and further calculates the acceleration in the film buckling process on the basis of calculating the speed and the displacement in the related technology, so as to obtain a more accurate simulation result, solve the problem that the deviation between the theoretical numerical value of the flexible electronic device and the actual condition is larger due to the calculation of the Green strain tensor, and improve the accuracy of the calculation of the theoretical numerical value of the flexible electronic device.
In one embodiment, fig. 10 is a block diagram of a second apparatus for membrane-based system buckling simulation according to an embodiment of the present invention, as shown in fig. 10, the apparatus further includes a circulation module 1002 and a stop module 1004:
and the circulating module 1002 is configured to obtain the displacement at the time t + △ t, the acceleration at the time t + △ t, and the speed at the time t + △ t according to the time step, the displacement at the time t, the acceleration at the time t, and the speed at the time t, where △ t is a time step.
A stopping module 1004 for stopping the simulation of the membrane based system if the time step accumulates for a period of time greater than a preset period of time.
Through the module 1002 and the module 1004, the circulation module 1002 circulates with a smaller time step △ t, and a film buckling simulation result is obtained through circulation calculation, so that the calculation result is more accurate, and the module 1004 stops simulation when the time period accumulated by the time step is greater than a preset time period, thereby further improving the accuracy of the theoretical numerical calculation of the flexible electronic device.
In one embodiment, fig. 11 is a schematic structural diagram of a film according to an embodiment of the present invention, as shown in fig. 11, where x represents axial displacement, y represents deflection, and Uy ═ 0 is a boundary condition applied at the right end, indicating that the displacement of the right end in the y direction is zero. The left end of the membrane structure was fixed and an axial pressure P of 100 was applied to the right end of the membrane for 1 s. The film structure has a predetermined mode of Asin (λ x), where a has a value of 0.1, λ ═ pi/10, geometric material parameters of length L ═ 10, thickness D ═ 0.1, young's modulus E ═ 3 × 105The poisson ratio μ is 0.1, and the density ρ is 1. FIG. 12 is a schematic representation of the mode shape of a membrane after buckling, as shown in FIG. 12, according to an embodiment of the invention.
In one embodiment, fig. 13 is a schematic diagram of a copper foil post-buckling analysis according to an embodiment of the present invention, as shown in fig. 13, where the horizontal axis is time t, the vertical axis is midpoint displacement Y, abaqus is a finite element calculation result, indicated by a dotted line, sr-meshfree is a result of a gridless calculation, indicated by a solid line, and the geometric material parameters of the copper foil are: length-thickness ratio L/D is 100, Young's modulus E is 120GPa, Poisson's ratio mu is 0.34, density rho is 8.96g/cm3. The left end of the copper foil is fixed, and the right end of the copper foil passes through displacementThe control applied a compression of 0.1L, with an initial defect of 0.1D, a compression of 0.1, and a duration of 1 s. The post-buckling behavior of the copper foil is described by a curve of the displacement of the midpoint of the copper foil along with the change of time, and the infinite element method adopted in the embodiment is consistent with the finite element (abaqus) result.
In one embodiment, FIG. 14 is a schematic diagram of a transient analysis of a thin film according to an embodiment of the present invention, as shown in FIG. 14, with the left end of the thin film structure fixed and an axial pressure of 100 applied to the right end of the thin film for a time of 1 s. The geometric material parameters of the film structure are that the length L is 10, the thickness D is 0.1, and the Young modulus E is 3 multiplied by 105The poisson ratio μ is 0.1, and the density ρ is 1. From fig. 14, it can be seen that the results calculated by the finite element and the gridless method are similar.
In one embodiment, a computer device is provided, which may be a terminal. The computer device includes a processor, a memory, a network interface, a display screen, and an input device connected by a system bus. Wherein the processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device comprises a nonvolatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of an operating system and computer programs in the non-volatile storage medium. The network interface of the computer device is used for communicating with an external terminal through a network connection. The computer program is executed by a processor to implement a method of membrane-based system buckling simulation. The display screen of the computer equipment can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer equipment can be a touch layer covered on the display screen, a key, a track ball or a touch pad arranged on the shell of the computer equipment, an external keyboard, a touch pad or a mouse and the like.
In one embodiment, fig. 15 is a schematic diagram of an internal structure of a computer device according to an embodiment of the present invention, and as shown in fig. 15, a computer device is provided, where the computer device may be a server, and the internal structure diagram may be as shown in fig. 15. The computer device includes a processor, a memory, a network interface, and a database connected by a system bus. Wherein the processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device comprises a nonvolatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of an operating system and computer programs in the non-volatile storage medium. The database of the computer device is used for storing data. The network interface of the computer device is used for communicating with an external terminal through a network connection. The computer program is executed by a processor to implement a method of membrane-based system buckling simulation.
Those skilled in the art will appreciate that the architecture shown in fig. 15 is merely a block diagram of some of the structures associated with the disclosed aspects and is not intended to limit the computing devices to which the disclosed aspects apply, as particular computing devices may include more or less components than those shown, or may combine certain components, or have a different arrangement of components.
In one embodiment, a computer device is provided, which includes a memory, a processor, and a computer program stored on the memory and executable on the processor, and the processor executes the computer program to implement the steps of the method for membrane-based system buckling simulation provided by the above embodiments.
In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored, which, when being executed by a processor, carries out the steps of the method for membrane-based system buckling simulation provided by the respective embodiments described above.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by hardware instructions of a computer program, which can be stored in a non-volatile computer-readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. Any reference to memory, storage, database, or other medium used in the embodiments provided herein may include non-volatile and/or volatile memory, among others. Non-volatile memory can include read-only memory (ROM), Programmable ROM (PROM), Electrically Programmable ROM (EPROM), Electrically Erasable Programmable ROM (EEPROM), or flash memory. Volatile memory can include Random Access Memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms such as Static RAM (SRAM), Dynamic RAM (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDRSDRAM), Enhanced SDRAM (ESDRAM), Synchronous Link DRAM (SLDRAM), Rambus Direct RAM (RDRAM), direct bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).
The technical features of the above embodiments can be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the above embodiments are not described, but should be considered as the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above examples only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (10)
1. A method of membrane-based system flexure simulation, the method comprising:
acquiring the initial speed, the initial characteristic matrix and the initial displacement of the thin film buckling, acquiring the initial acceleration according to the initial characteristic matrix and the initial displacement, and acquiring an integral constant according to the time step length of the thin film buckling;
obtaining an equivalent stiffness matrix at the time t according to the initial stiffness characteristic matrix and the integral constant, and obtaining an equivalent force vector at the time t according to the initial equivalent force characteristic matrix, the initial speed, the integral constant and the initial acceleration;
and obtaining the displacement increment of the film at the t moment according to the equivalent stiffness matrix at the t moment and the equivalent force vector at the t moment, obtaining the displacement at the t moment according to the initial displacement and the displacement increment at the t moment, obtaining the acceleration at the t moment according to the displacement increment at the t moment, the initial speed and the initial acceleration, and obtaining the speed at the t moment according to the initial speed, the initial acceleration and the acceleration at the t moment.
2. The method of film-based system flexure simulation of claim 1, wherein after obtaining the displacement at time t, obtaining the acceleration at time t, and obtaining the velocity at time t, the method further comprises:
obtaining displacement at the t + △ t moment, acceleration at the t + △ t moment and speed at the t + △ t moment according to the time step, the displacement at the t moment, the acceleration at the t moment and the speed at the t moment, wherein △ t is the time step;
stopping the simulation of the membrane-based system buckling in the event that the time step accumulates for a period of time greater than a preset period of time.
3. The method of film-based system buckling simulation of claim 2, wherein said deriving a displacement at time t + △ t, an acceleration at time t + △ t, and a velocity at time t + △ t from said time step, a displacement at time t, an acceleration at time t, and a velocity at time t comprises:
approximating the displacement increment of the t moment and the speed of the t moment according to a moving least square MLS difference shape function to obtain an approximate displacement increment and an approximate speed, wherein the boundary condition of the MLS difference shape function is an increment variational equation;
and obtaining approximate displacement according to the approximate displacement increment, and obtaining displacement at the t + △ t moment, acceleration at the t + △ t moment and speed at the t + △ t moment according to the time step, the approximate displacement, the acceleration at the t moment and the approximate speed.
4. The method of membrane-based system buckling simulation of claim 3, wherein the boundary condition of the MLS difference shape function is an incremental variational equation comprising:
the increment variational equation is obtained according to a penalty function method.
5. The method of film-based system buckling simulation of claim 1, wherein prior to said acquiring an initial velocity, an initial feature matrix, and an initial displacement of thin film buckling, the method comprises:
under the condition that the uniaxial buckling mode of the film is a cosine curve, acquiring axial displacement and deflection of the film in a towing coordinate system, wherein the deflection is obtained according to the amplitude and wave number of the buckling of the film;
and acquiring a strain tensor of the thin film according to the axial displacement and an average rotation angle of the buckling of the thin film, and acquiring a rotation tensor of the thin film through the average rotation angle, wherein the average rotation angle is obtained by a second component of the axial displacement in the towing coordinate system.
6. The method of claim 5, wherein the obtaining the deflection of the membrane comprises:
obtaining the bending energy of the thin film according to the amplitude, the wavelength of the thin film buckling and the geometric characteristics;
obtaining the film energy of the film according to the in-plane strain of the film and the geometrical characteristics, wherein the in-plane strain is obtained according to the strain tensor and the pre-applied strain;
and obtaining the amplitude and the wavelength according to the bending energy and the film energy, and obtaining the deflection according to the amplitude and the wavelength.
7. An apparatus for membrane-based system buckling simulation, the apparatus comprising an initialization module, an equivalence module, and a dynamics computation module:
the initial module is used for acquiring the initial speed, the initial characteristic matrix and the initial displacement of the thin film buckling, acquiring the initial acceleration according to the initial characteristic matrix and the initial displacement, and acquiring the integral constant according to the time step length of the thin film buckling;
the equivalent module is used for obtaining an equivalent stiffness matrix at the time t according to an initial stiffness characteristic matrix and the integral constant, and obtaining an equivalent force vector at the time t according to an initial equivalent force characteristic matrix, the initial speed, the integral constant and the initial acceleration;
the dynamics calculation module is used for obtaining the displacement increment of the film at the t moment according to the equivalent stiffness matrix at the t moment and the equivalent force vector at the t moment, obtaining the displacement at the t moment according to the initial displacement and the displacement increment at the t moment, obtaining the acceleration at the t moment according to the displacement increment at the t moment, the initial speed and the initial acceleration, and obtaining the speed at the t moment according to the initial speed, the initial acceleration and the acceleration at the t moment.
8. The apparatus of claim 7, further comprising a circulation module and a stop module:
the circulation module is used for obtaining displacement at the t + △ t moment, acceleration at the t + △ t moment and speed at the t + △ t moment according to the time step, the displacement at the t moment, the acceleration at the t moment and the speed at the t moment, wherein △ t is the time step;
the stopping module is used for stopping the simulation of the buckling of the membrane-based system when the accumulated time period of the time step is greater than a preset time period.
9. A computer device comprising a memory and a processor, the memory storing a computer program, wherein the processor implements the steps of the method of any one of claims 1 to 6 when executing the computer program.
10. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the steps of the method of any one of claims 1 to 6.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111797503A (en) * | 2020-06-05 | 2020-10-20 | 中国飞机强度研究所 | Method for controlling buckling of piezoelectric film connector |
| CN113092261A (en) * | 2021-05-20 | 2021-07-09 | 中国矿业大学 | Method for determining macroscopic and microscopic whole process of rock deformation destruction based on four-parameter test |
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2019
- 2019-12-30 CN CN201911399657.9A patent/CN111144020A/en active Pending
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111797503A (en) * | 2020-06-05 | 2020-10-20 | 中国飞机强度研究所 | Method for controlling buckling of piezoelectric film connector |
| CN111797503B (en) * | 2020-06-05 | 2023-10-20 | 中国飞机强度研究所 | Method for controlling piezoelectric film connector to break away from buckling |
| CN113092261A (en) * | 2021-05-20 | 2021-07-09 | 中国矿业大学 | Method for determining macroscopic and microscopic whole process of rock deformation destruction based on four-parameter test |
| CN113092261B (en) * | 2021-05-20 | 2021-11-05 | 中国矿业大学 | Method for determining macroscopic and microscopic whole process of rock deformation destruction based on four-parameter test |
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