CN111539138A - Method for solving time domain response sensitivity of structural dynamics peak value based on step function - Google Patents
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Abstract
The invention relates to a structural dynamics time domain response sensitivity solving method based on a step function, which comprises a time domain response peak value approximation method and an approximation function sensitivity solving method; the time domain response peak value is obtained by performing time integration on a step function taking a time domain response course as an independent variable to obtain an approximate value of the time domain response peak value; the approximation function sensitivity is achieved by the adjoint vector method. The method solves the problem that the subjective parameter selection of the peak value approximation method in the existing structural dynamics time domain topology optimization has large influence, has simple structure, easy programming and easy realization, and obviously improves the optimization efficiency.
Description
Technical Field
The invention belongs to the field of structural dynamics topology optimization, and particularly relates to an integration method for approximating a time domain response peak value through a step function and a sensitivity solving method for a peak value approximation value related to a related variable.
Background
The structure optimization design is divided into three stages of concept design, shape design and parameter design, wherein the most important stage is the concept design stage, the concept design determines the basic configuration of the structure, and the topology optimization is a tool widely applied in the concept design stage. Currently, the research on structural statics topology optimization is becoming mature day by day, but statics working conditions cannot cover all application scenarios in the complete life cycle of a structure, and therefore, structural dynamics topology optimization is currently a research hotspot. According to the time and frequency characteristics of design indexes, the structural dynamics topology optimization is divided into two branches of a frequency domain and a time domain, the frequency domain topology optimization can avoid large-scale calculation consumption of dynamics analysis and time domain history sensitivity solving, but can only realize the maximization of the dynamic stiffness of the structure, and cannot establish intuitive connection with the real value of the structural dynamics response time history.
The dynamic time-domain topology optimization takes the evaluation of the response time course as a research starting point, and can directly optimize the specific indexes of the response course. At present, response process evaluation indexes comprise an integral and a peak, the integral can evaluate the total amount of vibration, and also can not establish visual connection with a real numerical value of a structural dynamics response time process, the peak is the most visual index capable of representing structural dynamics response characteristics, peak proxy representation is usually carried out on the current peak dynamics topology optimization by a clustering function method, and the influence of subjectivity on an optimization result is large due to strong correlation of function parameters.
Disclosure of Invention
The technical problem solved by the invention is as follows: in order to overcome the defects of the prior art, the method for solving the time domain response sensitivity of the peak value of the structural dynamics based on the step function is provided, the method is composed of a time domain response peak value approximation equation based on the step function and a sensitivity solving method of the approximation equation about design variables, and the problems that the peak value time domain index of the existing structural time domain dynamics topology optimization is greatly influenced by subjective parameters and is difficult to converge are solved.
The technical scheme of the invention is as follows:
a method for solving the peak time-domain response sensitivity of the structure dynamics based on a step function comprises the following steps:
step (1), initializing an optimization model, establishing a finite element analysis model by taking a structural design domain as a geometric boundary, and multiplying the elastic modulus of the ith element by a pseudo density xiTo the power of p, where xi∈[0,1]P is 3, pseudo density x of all unitsiForming a design variable vector x, and extracting a structural rigidity matrix K,A quality matrix M for determining the constraint degree of freedom;
step (2), determining a load history F (t) borne by the structure, and defining a damping matrix of the finite element model in the step (1) as C- αcM+βcK，αcAnd βcIs a proportional damping coefficient;
and (3) solving the structural dynamic response of the finite element model constructed in the step (1) under the load environment and damping condition defined in the step (2) by a numerical solution method or an approximate analytic solution method of any differential equation, and acquiring a structural displacement field U (t) and a velocity field
Acceleration field
t is time;
step (4), according to the structure displacement field U (t) obtained in the step (3), establishing an attention index f (U (t)) of structure time domain dynamics topology optimization, combining f (U (t)), U (t) and Max (f (U (t)), solving a fixed integral through an arbitrary numerical integration method, and obtaining an approximate value of a dynamics response peak value Max (f (U (t)))
Solving the obtained dynamics time domain response peak value approximation value and returning to a topology optimization main program;
step (5), according to the structural displacement field U (t) obtained in the step (3), solving a first derivative matrix of the attention index of structural time domain dynamics topology optimization with respect to the structural displacement field
Combining F (U (t)), U (t) and Max (F (U (t))), solving the virtual load process Fλ(t), defining the virtual damping matrix of the finite element model in the step (1) as-C- αcM-βcK；
Step (6), solving the structure virtual dynamic response of the finite element model constructed in the step (1) under the virtual load environment and the virtual damping condition defined in the step (5) through a numerical solving method or an approximate analytic solving method of any differential equation, obtaining the structure virtual dynamic response lambda (tau), and naming the virtual dynamic response vector as an accompanying vector;
step (7), according to the displacement field U (t), the velocity field obtained in the step (3)
Acceleration field
Solving unit node displacement U with the serial number of ith unite,i(t) Unit node velocity
And unit node acceleration
Step (8) of solving the unit node accompanying vector lambda (t) numbered as the ith unit according to the accompanying vector lambda (t) obtained in the step (6)e,i(t)；
Step (9), solving the unit stiffness matrix K when the unit pseudo density is equal to 1 according to the structural stiffness matrix K obtained in the step (1), the mass matrix M and the damping matrix C obtained in the step (2)eCell mass matrix MeCell damping matrix Ce；
Step (10) of obtaining U based on steps (7) to (9)e,i(t)、
λe,i(t)、Ke、MeAnd CeSolving the constant integral through an arbitrary numerical integration method to obtain the approximate value of the dynamic time domain response index
Pseudo density x for the ith numbered celliThe sensitivity of (c);
and (11) repeating the steps (7) to (10) through serial operation or parallel operation until the sensitivity of the structure dynamics time domain response index approximation value relative to all unit pseudo densities is solved, completing the solution of the structure dynamics peak time domain relative to the sensitivity of the structure topology optimization design variable response, and returning the sensitivity of the dynamics time domain response peak approximation value obtained by solution to the topology optimization main program.
Furthermore, the method only relates to the approximate value of the structural dynamics peak time domain response index and the sensitivity solution of the structural dynamics peak time domain response index relative to all unit pseudo densities, and can be embedded into a gradient solution algorithm for topological optimization of any structure, and the parameters acquired in the step (1) can be realized by a method and a program platform for solving the structural dynamics.
Further, the structure displacement field U (t), the velocity field in the step (3)
And acceleration field
The method is obtained by solving the following differential equation system:
the system of differential equations in the above formula is a system of differential equations with initial conditions and no end conditions, and the initial conditions are that U (0) is 0
The above formula can be solved by a numerical solving method or an approximate analytic solving method of any differential equation.
Further, the approximation value of the dynamic peak time domain response f (U (t)) in the step (4)
Obtained by solving the following definite integral:
wherein e is natural index, β is χ -0.6,
x is far greater than
Positive real numbers of (d); Δ t is the integration step; t is tfFor the termination time of the kinetic analysis, the above equation can be solved by any numerical integration method.
Further, the virtual load history F in the step (5)λ(t) solving by the following equation
Further, the adjoint vector λ (t) in step (6) is obtained by solving the following differential equation system
The system of differential equations in the above formula is a system of differential equations with no initial condition but with a termination condition, and the termination condition is λ (t)f)＝0
The above formula can be solved by a numerical solving method or an approximate analytic solving method of any differential equation.
Further, the approximation value of the dynamic peak time domain response in the step (10)
Pseudo density x for the ith numbered celliThe sensitivity of (c) needs to be obtained by solving the following definite integral:
the above equation can be solved by any numerical integration method.
Compared with the prior art, the invention has the beneficial effects that:
(1) the method adopts a peak value approximation method of time domain response peak values based on step function integration, reduces approximation errors through a reference value translation strategy when a peak value approximation function is constructed, and can improve optimization speed when being suitable for the condition that the integration step length is large;
(2) the time domain response peak value approximation method based on step function integration has the advantages that the approximation value and the real function value have the same monotonicity, and the sensitivity in the same direction as the real value can be given in topology optimization;
(3) the invention does not relate to the step of dynamics solution, only relates to the approximate value of the structural dynamics peak value time domain response index and the sensitivity solution of the structural dynamics peak value time domain response index relative to all unit pseudo densities, and can be embedded into a gradient solution algorithm of any structural topology optimization;
(4) the accuracy of the peak value approximation value of the time domain response peak value based on the step function integration is not strong in dependence on the response process after the peak value response occurs, the response time length concerned by dynamics and sensitivity calculation can be shortened, and the optimization time consumption is reduced;
(5) the dynamic response peak value approximation and sensitivity solving method has good portability, can be combined with any numerical integration and differential equation system solving method in the aspect of solving, and can be combined with any pseudo density interpolation model and gradient optimization algorithm in the aspect of application.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a diagram of structural dimensions, loads and constraint environments in an embodiment of the present invention;
FIG. 3 is a time varying load history experienced by a structure in an embodiment of the present invention;
FIG. 4 is the structural statics topology optimization result of the present invention;
FIG. 5 is the optimization result of the structural time domain dynamics topology optimization embedded in the present invention under the condition that the termination time is 0.12s, 0.15s, 0.18s and 0.58s respectively;
FIG. 6 is a convergence history of the structural time domain dynamics topology optimization incorporating the present invention at termination times of 0.12s, 0.15s, 0.18s, and 0.58s, respectively;
FIG. 7 is a comparison of the dynamics response of the structural time domain dynamics topology optimization optimal solution and the statics topology optimization optimal solution embedded in the present invention.
Detailed Description
The invention is further illustrated by the following examples.
As shown in fig. 1, the invention provides a method for solving the peak time-domain response sensitivity of the structural dynamics based on a step function, which comprises the following steps:
step (1), initializing an optimization model, establishing a finite element analysis model by taking a structural design domain as a geometric boundary, and multiplying the elastic modulus of the ith element by a pseudo density xiTo the power of p, where xi∈[0,1]P is 3, pseudo density x of all unitsiForming a design variable vector x, extracting a structural rigidity matrix K and a quality matrix M according to a finite element model, and determining a constraint degree of freedom;
step (2), determining a load history F (t) borne by the structure, and defining a damping matrix of the finite element model in the step (1) as C- αcM+βcK，αcAnd βcIs a proportional damping coefficient;
step (3) obtaining a structural displacement field U (t), a speed field
Acceleration field
The structural dynamic response of the finite element model constructed in the step (1) under the load environment and the damping condition defined in the step (2) is solved, namely the following differential equation system is solved
The system of differential equations in the above formula is a system of differential equations with initial conditions and no end conditions, and the initial conditions are that U (0) is 0
The above formula can be solved by a numerical solving method or an approximate analytic solving method of any differential equation;
step (4), according to the structure displacement field U (t) obtained in the step (3), establishing an attention index f (U (t)) of structure time domain dynamics topological optimization, and combining f (U (t)), U (t) and Max (f (U (t)), and an approximate value of a dynamics response peak value Max (f (U (t)))
Can be obtained by solving the following equation
Wherein e is natural index, β is χ -0.6,
x is far greater than
Positive real numbers of (d); Δ t is the integration step; t is tfThe termination time of the kinetic analysis. The above formula can be carried out by any numerical integration method, and the dynamics time domain response peak value approximation value obtained by solving and solving is returned to the topology optimization main program.
Step (5), according to the structural displacement field U (t) obtained in the step (3), solving a first derivative matrix of the attention index of structural time domain dynamics topology optimization with respect to the structural displacement field
Combining F (U (t)), U (t) and Max (F (U (t))), the virtual load process Fλ(t) can be solved by the following formula
After the virtual load history is solved, defining the virtual damping matrix of the finite element model in the step (1) as-C- αcM-βcK；
Step (6) of obtaining an accompanying vector lambda (tau), and solving the structural virtual dynamic response of the finite element model constructed in the step (1) under the virtual load environment and the virtual damping condition defined in the step (5) in a required mode, namely solving the following differential equation system
The system of differential equations in the above formula is a system of differential equations with no initial condition but with a termination condition, and the termination condition is λ (t)f)＝0
The above formula can be solved by a numerical solving method or an approximate analytic solving method of any differential equation;
step (7), according to the displacement field U (t), the velocity field obtained in the step (3)
Acceleration field
Extracting unit node displacement U with the serial number of the ith unite,i(t) Unit node velocity
And unit node acceleration
Step (8) of extracting the unit node accompanying vector lambda (t) with the number of the ith unit according to the accompanying vector lambda (t) obtained in the step (6)e,i(t)；
Step (9), obtaining the knot according to the step (1)Constructing a stiffness matrix K, a mass matrix M and a damping matrix C obtained in the step (2), and solving the unit stiffness matrix K when the unit pseudo density is equal to 1eCell mass matrix MeCell damping matrix Ce；
Step (10) of obtaining U based on steps (7) to (9)e,i(t)、
λe,i(t)、Ke、MeAnd CeApproximation of the dynamic peak time-domain response
Pseudo density x for the ith numbered celliThe sensitivity of (D) is obtained by solving the following constant integral
The above formula can be solved by any numerical integration method;
and (11) repeating the steps (7) to (10) through serial operation or parallel operation until the sensitivity of the structural dynamics time domain response index approximate value about all unit pseudo densities is solved, and returning the sensitivity of the dynamics time domain response peak value approximate value obtained by solving to a topology optimization main program.
Examples
In order to fully understand the characteristics of the invention and the applicability of the invention to engineering practice, the invention establishes a structure and load constraint environment as shown in the figure, and embeds the structure and load constraint environment into the time domain topological optimization of continuum structure dynamics, the optimization adopts a gradient algorithm moving asymptote method MMA, a pseudo density interpolation model adopts a SIMP model with p being 6, the optimization target is the minimum time domain response peak value, the optimization constraint is that the area ratio is not less than 0.3, and the method provided by the invention is embedded into a main program framework of topological optimization to solve the optimization target and the sensitivity of the optimization target. The specific values of the parameters in each real-time step are as follows:
the domain design in step (1) is shown in FIG. 2The design domain size is 100mm × 70mm, the structural finite element model is 100 units in the longitudinal direction and 70 units in the transverse direction, the unit numbers of the longitudinal direction and the transverse direction are started from the upper left corner, and the Young modulus is 2 × 105Mpa, density 7.8 × 10-6Kg/mm3, Poisson's ratio of 0.3, cell type using planar bilinear cells.
Proportional damping coefficient α in step (2)C10 and βC＝1×10-5(ii) a The structure is restrained at the lower two end points, the structure is subjected to two time-varying loads along the X direction and the Y direction at the upper right corner node of the 17 th unit in the 1 st row, a 0.1Kg counterweight is attached to a loaded point, the load process is shown in figure 3, the maximum value of the load in the X direction appears at 0.062s, and the maximum value of the load in the Y direction appears at 0.082 s.
And (3) solving a kinetic differential equation by adopting a New Mark-beta method, wherein the calculation step length delta t is 0.001s, and in order to verify that the dependence of the method on the analysis duration is not strong, the kinetic analysis and the corresponding topology optimization are respectively carried out under 4 groups of termination times of 0.12s, 0.15s, 0.18s and 0.58 s.
The dynamic time domain index f (U (t)) concerned in the step (4) is the sum of the maximum displacement of the structure loaded node in the X direction and the maximum displacement of the structure loaded node in the Y direction, namely
Wherein
Is an output vector which is a column vector with the same degree of freedom, the corresponding position of the translational degree of freedom of the loaded node in the X direction is 1, other positions are 0,
is an output vector which is a column vector with the same degree of freedom, the corresponding position of the translation degree of freedom of the loaded node in the Y direction is 1, the other positions are 0, β is 20, and χ is 10000, then
The definite integral is solved by adopting a trapezoidal method, and the correspondingIn step (3), the integration step Δ t is 0.001s, tf0.12s, 0.15s, 0.18s and 0.58s, respectively.
And (5) solving according to the formula provided by the invention without parameter input.
Step (6) adopts a New Mark- β method to solve a kinetic differential equation, corresponding to step (3), delta t is 0.001s, tf0.12s, 0.15s, 0.18s and 0.58s, respectively.
Step (7) extracting according to the logic and the sequence of the unit and node numbers without inputting parameters;
step (8), extracting according to the logic and the sequence of the unit and node numbers without inputting parameters;
and (9) no parameter input is needed, and the unit type adopts a planar bilinear unit.
The definite integral in the step (10) is solved by adopting a trapezoidal method, corresponding to the step (3), the integral step length delta t is 0.001s, tf0.12s, 0.15s, 0.18s and 0.58s, respectively.
And (11) repeating the steps (7) to (10) until all the units are calculated, and solving the sensitivity of the obtained dynamics time domain response peak value approximate value and returning the sensitivity to the topology optimization main program.
And (3) after all the steps are finished, returning the approximation value of the time domain response peak calculated in the step (4) and the sensitivity of the time domain response peak approximation value calculated in the step (11) to a topology optimization group program, adjusting the next pseudo density distribution by moving an asymptote algorithm MMA, performing the real-time steps of the method again after the adjustment, and repeating the steps (1) to (11) until the structure time domain dynamics topology optimization converges.
In order to verify that the time domain response peak value approximation method and the corresponding sensitivity solving method provided by the invention can effectively operate in a structural dynamics time domain topology optimization framework and can reduce the structural dynamics time domain response peak value, the embodiment adopts statics topology optimization aiming at the same model, the load environment is a static load, the X-direction environmental load and the Y-direction static load are the peak values of the load process in the step (2), and other constraint environments and optimization algorithms are consistent with the structural dynamics topology optimization.
It can be seen from comparison between fig. 4 and fig. 5 that the topology configuration of the solution optimized by the statics topology is different from the topology configuration of the solution optimized by the dynamics topology, and the topology configuration of the solution optimized by the structure dynamics topology based on the present invention does not depend on the time length of the dynamics analysis, and it can also be seen from fig. 6 that the optimization can be converged quickly and the convergence values are completely the same no matter how long the time length of the dynamics analysis is. As can be seen from fig. 7, the peak value of the dynamic response of the statics topology optimization optimal configuration is greater than the peak value of the dynamic response of the dynamics topology optimization optimal configuration embedded in the present invention, which shows that the method for solving the time domain response sensitivity of the structural dynamics peak value based on the step function provided by the present invention can be very effectively embedded in the gradient topology optimization method, and can effectively reduce the peak value of the time domain response.
The invention adopts a peak value approximation method of time domain response peak value based on step function integration, and reduces approximation error through a reference value translation strategy when constructing a peak value approximation function, thereby being applicable to the condition of larger integration step length and improving optimization speed.
The time domain response peak value approximation method based on step function integration has the advantages that the approximation value and the real function value have the same monotonicity, and the sensitivity in the same direction as the real value can be given in topology optimization.
Although the present invention has been described with reference to preferred embodiments, it is not intended to be limited thereto, and those skilled in the art can make modifications and variations to the disclosed methods and techniques without departing from the spirit and scope of the present invention. Therefore, any simple modification, equivalent change and modification of the above embodiments according to the technical essence of the present invention are within the protection scope of the technical solution of the present invention, unless departing from the content of the technical solution of the present invention.
Claims (7)
1. A structural dynamics peak time domain response sensitivity solving method based on a step function is characterized by comprising the following steps:
step (1), initializing an optimization model, establishing a finite element analysis model by taking a structural design domain as a geometric boundary, and multiplying the elastic modulus of the ith element by a pseudo density xiTo the power of p, where xi∈[0,1]P is 3, pseudo density x of all unitsiForming a design variable vector x, extracting a structural rigidity matrix K and a quality matrix M according to a finite element model, and determining a constraint degree of freedom;
step (2), determining a load history F (t) borne by the structure, and defining a damping matrix of the finite element model in the step (1) as C- αcM+βcK，αcAnd βcIs a proportional damping coefficient;
and (3) solving the structural dynamic response of the finite element model constructed in the step (1) under the load environment and damping condition defined in the step (2) by a numerical solution method or an approximate analytic solution method of any differential equation, and acquiring a structural displacement field U (t) and a velocity field
Acceleration field
t is time;
step (4), according to the structure displacement field U (t) obtained in the step (3), establishing an attention index f (U (t)) of structure time domain dynamics topology optimization, combining f (U (t)), U (t) and Max (f (U (t)), solving a fixed integral through an arbitrary numerical integration method, and obtaining an approximate value of a dynamics response peak value Max (f (U (t)))
Solving the obtained dynamics time domain response peak value approximation value and returning to a topology optimization main program;
step (5), according to the structural displacement field U (t) obtained in the step (3), solving a first derivative matrix of the attention index of structural time domain dynamics topology optimization with respect to the structural displacement field
Combining F (U (t)), U (t) and Max (F (U (t))), solving the virtual load process Fλ(t), defining the virtual damping matrix of the finite element model in the step (1) as-C- αcM-βcK；
Step (6), solving the structure virtual dynamic response of the finite element model constructed in the step (1) under the virtual load environment and the virtual damping condition defined in the step (5) through a numerical solving method or an approximate analytic solving method of any differential equation, obtaining the structure virtual dynamic response lambda (tau), and naming the virtual dynamic response vector as an accompanying vector;
step (7), according to the displacement field U (t), the velocity field obtained in the step (3)
Acceleration field
Solving unit node displacement U with the serial number of ith unite,i(t) Unit node velocity
And unit node acceleration
Step (8) of solving the unit node accompanying vector lambda (t) numbered as the ith unit according to the accompanying vector lambda (t) obtained in the step (6)e,i(t)；
Step (9), solving the unit stiffness matrix K when the unit pseudo density is equal to 1 according to the structural stiffness matrix K obtained in the step (1), the mass matrix M and the damping matrix C obtained in the step (2)eCell mass matrix MeCell damping matrix Ce；
Step (10) of obtaining U based on steps (7) to (9)e,i(t)、
λe,i(t)、Ke、MeAnd CeSolving the constant integral through an arbitrary numerical integration method to obtain the approximate value of the dynamic time domain response index
Pseudo density x for the ith numbered celliThe sensitivity of (c);
and (11) repeating the steps (7) to (10) through serial operation or parallel operation until the sensitivity of the structure dynamics time domain response index approximation value relative to all unit pseudo densities is solved, completing the solution of the structure dynamics peak time domain relative to the sensitivity of the structure topology optimization design variable response, and returning the sensitivity of the dynamics time domain response peak approximation value obtained by solution to the topology optimization main program.
2. The method for solving the peak time-domain response sensitivity of the step function-based structure dynamics according to claim 1, wherein: the method only relates to an approximate value of a structural dynamics peak value time domain response index and sensitivity solving of the approximate value of the structural dynamics peak value time domain response index and all unit pseudo densities, and can be embedded into a gradient solving algorithm of any structural topology optimization, and parameters acquired in the step (1) can be realized through a any structural dynamics solving method and a program platform.
3. The method for solving the peak time-domain response sensitivity of the step function-based structure dynamics according to claim 1, wherein: structural displacement field U (t), velocity field in step (3)
And acceleration field
The method is obtained by solving the following differential equation system:
the system of differential equations in the above formula is a system of differential equations with initial conditions and no end conditions, and the initial conditions are that U (0) is 0
The above formula can be solved by a numerical solving method or an approximate analytic solving method of any differential equation.
4. The method for solving the peak time-domain response sensitivity of the step function-based structure dynamics according to claim 1, wherein: approximation value of dynamics peak time domain response f (U (t)) in step (4)
Obtained by solving the following definite integral:
wherein e is natural index, β is χ -0.6,
x is far greater than
Positive real numbers of (d); Δ t is the integration step; t is tfFor the termination time of the kinetic analysis, the above equation can be solved by any numerical integration method.
5. The method for solving the peak time-domain response sensitivity of the step function-based structure dynamics according to claim 4, wherein: virtual load history F in step (5)λ(t) solving by the following equation
6. The method for solving the peak time-domain response sensitivity of the step function-based structure dynamics according to claim 1, wherein: the adjoint vector λ (t) in step (6) is obtained by solving the following system of differential equations
The system of differential equations in the above formula is a system of differential equations with no initial condition but with a termination condition, and the termination condition is λ (t)f)＝0
The above formula can be solved by a numerical solving method or an approximate analytic solving method of any differential equation.
7. The method for solving the peak time-domain response sensitivity of the step function-based structure dynamics according to claim 1, wherein: approximation value of dynamics peak time domain response in step (10)
Pseudo density x for the ith numbered celliThe sensitivity of (c) needs to be obtained by solving the following definite integral:
the above equation can be solved by any numerical integration method.
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106650148A (en) * | 2016-12-30 | 2017-05-10 | 北京航空航天大学 | Method of continuum structure non-probabilistic reliability topological optimization under mixed constraints of displacements and stresses |
| CN107942664A (en) * | 2017-11-23 | 2018-04-20 | 中国南方电网有限责任公司 | A kind of hydrogovernor parameter tuning method and system based on sensitivity analysis |
| US20190080040A1 (en) * | 2017-09-13 | 2019-03-14 | Dalian University Of Technology | Integration method for accurate modeling and analysis and reliability-based design optimization of variable stiffness composite plate and shell structures |
| CN109508495A (en) * | 2018-11-12 | 2019-03-22 | 华东交通大学 | A kind of compliant mechanism overall situation stress constraint Topology Optimization Method based on K-S function |
| CN110442971A (en) * | 2019-08-06 | 2019-11-12 | 东北大学 | A kind of rotating cylindrical shell kinetic characteristics Uncertainty Analysis Method |
-
2020
- 2020-03-31 CN CN202010245755.3A patent/CN111539138B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106650148A (en) * | 2016-12-30 | 2017-05-10 | 北京航空航天大学 | Method of continuum structure non-probabilistic reliability topological optimization under mixed constraints of displacements and stresses |
| US20190080040A1 (en) * | 2017-09-13 | 2019-03-14 | Dalian University Of Technology | Integration method for accurate modeling and analysis and reliability-based design optimization of variable stiffness composite plate and shell structures |
| CN107942664A (en) * | 2017-11-23 | 2018-04-20 | 中国南方电网有限责任公司 | A kind of hydrogovernor parameter tuning method and system based on sensitivity analysis |
| CN109508495A (en) * | 2018-11-12 | 2019-03-22 | 华东交通大学 | A kind of compliant mechanism overall situation stress constraint Topology Optimization Method based on K-S function |
| CN110442971A (en) * | 2019-08-06 | 2019-11-12 | 东北大学 | A kind of rotating cylindrical shell kinetic characteristics Uncertainty Analysis Method |
Non-Patent Citations (1)
| Title |
|---|
| 李目;何怡刚;吴笑锋;王俊年;: "基于奇异值分解的分数阶小波综合实现方法", 电子测量与仪器学报 * |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112084174A (en) * | 2020-09-17 | 2020-12-15 | 西安交通大学 | Rapid establishing method for steam turbine set shafting fault diagnosis database |
| CN112084174B (en) * | 2020-09-17 | 2022-10-25 | 西安交通大学 | Rapid establishing method for steam turbine set shafting fault diagnosis database |
| CN112836166A (en) * | 2021-01-15 | 2021-05-25 | 北京科技大学 | Response peak analysis-based first-order differential algorithm for monitoring data of equal sampling experiment |
| CN112836166B (en) * | 2021-01-15 | 2023-12-01 | 北京科技大学 | First-order differential algorithm of monitoring data of equal-sampling experiment based on response peak analysis |
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