CN100377152C - Method for confirming stress intensity factor distribution on member crack tip - Google Patents
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Abstract
The present invention relates to a method for determining the factor distribution of the crack front stress intensity of a structural member. The method comprises the following steps that a heat load, a surface force load and a body force load which are borne by the structural member are provided, and simultaneously, a basic equation of a general weight function method is also provided under the signal action or the common action of the three loads; the crack front is divided into arbitrary N-1 sub-segments by N nodes, and a basic interpolation function Nj (s) and a partial variation function N'j (s) are introduced at each node j; the novel number value of the basic equation (containing an integral equation of the variation) of the general weight function method is approximately figured out by making use of a particular limited partial variation mode and a particular interpolation mode under the condition of the signal action or the common action of the heat load, the surface force load and the body force load. Thus, the factor distribution of the curve type 3D crack front stress intensity along the crack front is determined in a high precision and efficiency way, and moreover, compared with other existing methods, the actual operating efficiency of the method is enhanced to scores of times, or even hundreds of times.
Description
(I) the technical field
The invention relates to a method for determining the stress intensity factor distribution of a structural member crack front edge in the field of structural safety analysis and evaluation and a computer program design method, which are used for determining the distribution of the stress intensity factor (K) of a three-dimensional crack front edge in a structural member along the crack front edge in a structural safety evaluation process with high precision and high efficiency.
(II) background of the invention
Conventionally, there are two methods for determining the stress intensity factor distribution of the crack front in a structural member by computer calculation. One is an elastic mechanics direct method, which needs to calculate the elastic mechanics of the body with the crack first and determine the displacement field or stress field under the action of load; and then according to the obtained displacement field or stress field, calculating and determining the K value at each point of the front edge of the crack point by point. The specific calculation and determination method comprises a stress field singularity method, a crack surface opening displacement method, a J integral method and the like. The method has the disadvantages of low efficiency, particularly when the load is variable load changing along with time, elastic mechanical calculation (such as finite element method or boundary element method calculation) needs to be carried out on the body with the crack at each time point, and a displacement field or a stress field under the action of the load at the time point is determined; and then, according to the displacement field or the stress field at the moment, calculating and determining the K value point by a method of solving the opening displacement of the crack surface at the limit or solving the J integral at each point of the front edge of the crack. For engineering problems, the total efficiency is low because the workload of each finite element method or boundary element method calculation is large. The second method is a stress weight function method based on the superposition principle, and elastic mechanics calculation (for example, finite element method or boundary element method calculation) needs to be carried out on a body without a crack at first, and a stress field under the action of a load is determined; then, applying the obtained negative value of the stress to a crack surface by utilizing the superposition principle; and determining the K value at each point of the crack front edge through the integral of the product of the force load on the crack surface and the stress weight function according to the pre-calculated stress weight function on the crack surface of the crack body. The literature implementing this method is generally referred to simply as the weight function method. But in practice it is only applicable to the case where a face force load is applied to the crack face, and other loads (such as temperature load or volume force load) cannot be determined by calculation. The weight method described in these documents shall therefore be referred to exactly as the stress weight method or the surface force weight method, which is different from the general weight method described in the patent application, which can take into account temperature loads, surface force loads and volume force loads at the same time. This method is also inefficient when the load is a time varying variable load. Since it is also necessary to repeatedly perform elasto-mechanical calculations (e.g. finite element or boundary element calculations) on the body without cracks, determine the stress field under load at each moment, and then determine the K value at that moment by means of integral calculations.
Generally, the stress-weight method is only applied to shapes with relatively simple geometry (or can be handled with simplicity); when the method is used, an approximate expression of a stress weight function at each point on a crack surface is generally required to be firstly obtained. This is only possible in the case of relatively simple shapes, but is difficult to achieve in the case of relatively complex shapes or crack geometries. For the situation that the geometric shape is relatively complex, methods such as a finite element approximation method, a rigidity array derivative method, a slicing method and the like are needed to determine the weight function; the K value can then be determined by integrating the product of the surface force load and the weight function. In this respect, methods such as a finite element approximation method, a rigidity array derivative method, a slicing method and the like are only suitable for solving the problem of the front edge of the linear crack for the three-dimensional crack; for curved crack leading edge problems (such as elliptical, semi-elliptical and partially elliptical deep-seated cracks or surface crack problems), the mathematical simulation results are quite poor; the calculation result shows that the precision is lower. Moreover, the methods can obtain more satisfactory results for simpler load conditions, namely the condition that the distribution change of the stress intensity factors along the front edge of the crack is relatively flat; however, for a complicated load situation, i.e. a situation where the distribution of the stress intensity factor along the crack front edge changes more severely, the error is large, the accuracy is low, and the effect is poor.
The prior art has the following defects: (1) The efficiency of solving the stress intensity factor K value by the direct elastomechanics method is low; (2) The stress weight function method based on the superposition principle has low calculation efficiency for the variable load condition changing along with time, and is not suitable for temperature load and volume force load; (3) In the commonly used methods such as a finite element approximation method, a rigidity array derivative method, a slicing method and the like in the stress weight function method, for the problem of the curve type crack front edge, the mathematical simulation effect is poor, and the precision is low; (4) In the commonly used methods such as finite element approximation, rigid matrix derivative, and slicing among the stress weight function methods, the calculation error is large, and the accuracy is low, for the case where the distribution change of the stress intensity factor along the crack front edge is severe.
Disclosure of the invention
In order to overcome the defects of low calculation efficiency, poor mathematical simulation effect and low precision of the existing method for determining the stress intensity factor distribution of the front edge of the structural member crack, the invention provides a unique method for determining the stress intensity factor distribution of the front edge of the structural member crack, which can determine the distribution of the stress intensity factor of the curved three-dimensional crack front edge along the front edge of the crack with high precision and high efficiency; the actual execution efficiency of the method can be improved by dozens of times or even hundreds of times compared with the prior other methods.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a method for determining stress intensity factor distribution of a structural member crack front edge mainly comprises the following steps:
(1) Giving out the thermal load, the surface force load and the volume force load born by the structural member, and a general weight function method basic equation under the independent or combined action of the three loads, wherein the general weight function method basic equation is as shown in a formula (1):
wherein the variation symbol delta c A first-order deflection component representing each physical quantity with respect to a crack position; u. of (1) 、t (1) And K I (1) Respectively is a displacement function, a boundary surface force function and an I-type stress intensity factor distribution function when an arbitrary reference load (1) acts; u. of *(2) 、t *(2) 、f *(2) 、Θ *(2) And K I (2) Respectively serving as a boundary displacement function, a boundary surface force function, a volume force function, a temperature distribution function and an I-type stress intensity factor distribution function along the front edge of the crack when the load (2) to be solved acts; E. nu, H and alpha are respectively the elastic modulus, poisson's ratio, equivalent elastic constant and thermal expansion coefficient of the material; Γ is the crack front and s is the arc length along the crack front; sigma t 、∑ u Sigma and V are respectively the known boundary of face force, the known boundary of displacement, and the bodyA boundary and a volume of a body; n is the external normal vectorAn amount;
(2) Dividing the crack front edge into any N-1 subsegments by using N nodes, and introducing a basic interpolation type function N at each node j j (s) and a local variation function N j '(s) which both satisfy the conditional formula (2):
(3) The stress intensity factor K I (2) The distribution function along the crack front is expressed by equations (3), (4):
wherein K is I (1) Is a stress intensity factor distribution function under the action of a certain reference load;
(4) Introducing a macroscopic fundamental variation mode delta to the whole crack front c a s 0 As shown in formula (5):
wherein, delta c a is the variation of a characteristic crack length a, which is delta c a s 0 G(s) is a dimensionless spread function;
(5) Introducing N local variation modes at N nodes, wherein the N local variation modes are as shown in a formula (6):
wherein N is j '(s) is a local variation function;
(6) For the N local variation modes, listing N equations and calculating the integral of the right end of the equation to obtain the integral related to A i The system of linear equations of (1), equation (7):
(7) Solving for the unknown coefficient A i The system of linear equations (7); then substituting human formula (4) and formula (3) to obtain stress intensity factor K I (2) Distribution along the crack front.
Further, the method also includes:
(8) From K I (1) The approximate estimation value of (2) is calculated by the steps (1) to (7) to obtain K corresponding to the reference load I (2) Then, a new accurate reference load stress intensity factor distribution function K is obtained by using the following formula (8) I
Still further, the method further comprises:
(9) The obtained new K I (1) Exact solution of delta c (…)/δ c a, directly substituting the heat load, the surface force load and the volume force load into a formula (7), solving the equation set again, and solving the stress intensity factor distribution function K under the action of any heat load, surface force load and volume force load I (2) The numerical solution of (c).
Still further, said basic interpolation type function N j (s) and a local variation function N j '(s) are taken to be the same function.
Or, the basic interpolation type function N j (s) sum local variation function N j '(s) are taken as different functions.
Further, said basic interpolation type function N j (s) sum local variation function N j '(s), taking the linear mode of linear function, requires N points.
Or, the basic interpolation type function N j (s) and a local variation function N j '(s) is taken as an L-order function of the high-order mode, L is a natural number, L is more than or equal to 2, N = LM +1 points are needed, and M is a positive integer.
The working principle of the invention is as follows: a totally new type numerical determination method for approximately solving a general weight function method basic equation (an integral equation containing macroscopic variational factors, called a variational integral equation) under the condition of independent action or combined action of heat load, surface force load and volume force load by using a limited number of special local variational modes and a special interpolation mode is called as a finite variational method; used for solving the stress intensity of the three-dimensional crack front edge under the conditions of single action or combined action of thermal load, surface force load and volume force load with high precision and high efficiencyDistribution function K of factor along crack front I (2) The numerical solution of (c). The key points of the technical scheme are that a general weight function method basic equation (variational integral equation) under the condition of independent action or combined action of heat load, surface force load and volume force load is established; dividing a macroscopic variational domain into limited sub-variational domains; meanwhile, based on the discrete segmentation, a special basic interpolation function and a special local variation function are constructed; then, the basic interpolation functions are utilized to carry out the function on the distribution function K of the stress intensity factor of the three-dimensional crack front edge along the crack front edge under the condition that the thermal load, the surface force load and the volume force load act independently or jointly I (2) ) Carrying out discretization interpolation processing; simultaneously, introducing a basic variation mode defined on the whole macroscopic variation domain, and constructing and generating a limited number of local variation modes by using a local variation function; and then, for the finite variation modes generated in the way, integral calculation is carried out on a basic equation (variation integral equation) to form a unique linear equation system (narrow-band coefficient matrix with strong diagonal advantage) with very good calculation performance. By solving the system of linear equations, the distribution of the variables to be solved along the macroscopic variation domain (crack front) can be determined. By utilizing the self-consistency of the method, the distribution function K of the stress intensity factor along the front edge of the crack under the action of any reference load (thermal load, surface force load or volume force load) can be directly obtained I (1) The most reasonable and accurate numerical solution. The most reasonable and accurate numerical solution is substituted into the linear equation set formed above again, so that the variable K to be solved can be determined with high precision and high efficiency I (2) Numerical solution of the entire profile along the macroscopic variation domain (crack front).
After the distribution of the stress intensity factor K is determined, the stress intensity factor K can be compared with the fracture toughness Kc of the material to determine the safety of the structural part; or, the fatigue strength can be checked according to the variation range of K, and the fatigue life can be determined. The actual execution efficiency of the method can be improved by dozens of times or hundreds of times compared with the prior other methods; especially in the case of impact loading, the stress intensity factor distribution determination task which can be completed by other methods in the prior art takes weeks to months, and can be completed within minutes to hours by the method.
Compared with the prior art, the invention has the following beneficial effects:
(1) And has high precision. Because the linear system obtained according to the method has good numerical computation performance. For example, when a basic interpolation function and a local variation function of a linear mode are adopted, a coefficient matrix of an equation set is a tri-diagonal matrix, and diagonal elements are large numbers; by two andfundamental interpolation of upper modesWhen the type function and the local variation function are used, the coefficient matrix of the equation set is a narrow-band coefficient matrix with strong diagonal advantage; thus K I (1) The local error of (2) and the error of the local point where the basic equation does not hold only affect the calculation results of the adjacent points, and do not affect the calculation results of the farther points, i.e. the local error is not expanded to the farther points.
(2) Reference load stress intensity factor distribution K obtained from self-consistency condition I (1) The most reasonable, precise numerical solution for the particular structural discretization used, or may be referred to as a numerical analytical solution. Therefore, it is substituted into K calculated by the linear equation system again I (2) The calculation of (c) will have the best accuracy.
(3) It has extremely high determination efficiency for the problem of load variation with time, such as for the case of thermal shock, surface force impact or volume force impact loads, or for other cases of stress intensity factor distribution variation with time. For the situations, the repeated stress field analysis or displacement field analysis and calculation which is required in the traditional direct elastic mechanics method or the stress weight function method based on the superposition principle can be avoided, the integral of the product of the load and the universal weight function is directly utilized to determine the change of the distribution of the stress intensity factor of the whole crack front edge along with the time, the determination process is greatly simplified, and the efficiency is greatly improved. The actual execution efficiency of the finite variation method can be improved by dozens of times or even hundreds of times compared with the prior other methods; especially for the case of impact loading, the stress intensity factor distribution determination task which can be completed by other methods in the prior art only within weeks or even months can be completed by the method within minutes to hours.
(4) For a specific problem, an infinite number of linearly independent local variation modes and basic interpolation type functions can be introduced. Therefore, the finite variation method has good numerical simulation capability and high precision for the complex case that the stress intensity factor changes along the crack front edge sharply. The macro variable domains can be reasonably segmented according to the specific situation of the specific problem and the specific requirement of precision; in places with drastic changes of stress intensity factors, the division points can be dense; in the place where the change of the stress intensity factor is relatively smooth, the division points can be sparse; besides linear mode functions, basic interpolation type functions and local variation functions of quadratic or higher order modes can be introduced where the accuracy requirement is high. Therefore, the specific calculation format can be flexibly adjusted according to the specific situation of the specific problem, and higher precision is achieved.
(5) The method is not only suitable for surface force load on a crack surface, but also suitable for the conditions of temperature load, non-crack surface force load and volume force load. For all these loads, the distribution of the stress intensity factor can be determined directly by the integral of the product of the load and the universal weight function using the basic equation.
(6) The method is not limited by the complexity of geometrical conditions. For the situation that the shape and the shape of the body or the geometry of the crack are complex, an analytical expression or an approximate expression of the weight function does not need to be solved, and the general weight function in the form of a numerical solution can be calculated by directly utilizing the displacement field solution of a finite element method or a boundary element method; the distribution of the stress intensity factor is then directly determined by the integral of the product of the load and the universal weight function using the fundamental equation.
(7) The method has good numerical simulation and solving capability for the three-dimensional crack problem (such as ellipse, semi-ellipse and partial ellipse deep-buried crack or surface crack problems) of the curve type crack front edge, and can obtain high precision.
(IV) description of the drawings
Fig. 1 shows a flow chart of a method for determining a stress intensity factor distribution of a crack front of a structural member.
FIG. 2 shows the basicVariation mode delta c a s 0 And local variation mode delta c a s j (linear mode is taken as an example) and the relationship between them.
FIG. 3 shows a local variation function and a basic interpolation function N j (s) (linear mode) construction method.
FIG. 4 shows a local variation function and a basic interpolation function N j (s) (secondary mode) construction method.
FIG. 5 shows a local variation function and a basic interpolation function N j (s) (L-order mode, take 3-order mode as an example).
FIG. 6 shows the results of the determination of the time-dependent change in stress intensity factor distribution of the crack front under thermal shock for a semi-elliptical surface crack in the flat plate of example 2.
Fig. 7 shows the determination result of the change process of the stress intensity factor distribution of the crack front edge with time under the simultaneous action of thermal shock and pressure shock (pressure-bearing thermal shock) of the axial semielliptical surface crack in the round pipe of the example 3.
(V) detailed description of the preferred embodiments
The invention is further described below with reference to the accompanying drawings.
Example 1
Referring to fig. 1, 2, 3, 4 and 5, a method for determining stress intensity factor distribution of a structural member crack front edge mainly comprises the following steps (see fig. 1):
(1) General weight function basic equation (variational integral equation) including thermal load, surface force load and volume force load for giving variation form of solved problem
Wherein the variation symbol delta c (\8230;) represents the first order variation of the physical quantity (\8230;) with respect to crack location, i.e., the physical quantity (\8230;) is a function of crack location as well as other variables, but only the first order variation when the crack location changes. u. of (1) 、t (1) And K I (1) Respectively a displacement function, a boundary surface force function and an I-type stress intensity factor distribution function when an arbitrary reference load (the upper mark is 1) acts; u. of *(2) 、t *(2) 、f *(2) 、Θ *(2) And K I (2) Respectively a boundary displacement function, a boundary surface force function, a volume force function, a temperature distribution function and an I-type stress intensity factor distribution function along the front edge of the crack when a load (the upper mark is expressed as 2) to be solved acts; E. ν, H and α are the elastic modulus, poisson's ratio, equivalent elastic constant and coefficient of thermal expansion of the material, respectively. Γ is the crack front and s is the arc length along the crack front; sigma t 、∑ u Σ, and V are the known boundary of face force, the known boundary of displacement, the body boundary, and the body volume, respectively; n is the outer normal vector.
(2) And dividing the crack front into any N-1 subsegments by using N nodes (see the attached figure 2). Introducing a basic interpolation type function N at each node j j (s) and a local variation function N j '(s) (see FIG. 2, FIG. 3, FIG. 4, FIG. 5) which all satisfy the condition
(3) The unknown quantity to be determined (stress intensity factor K) I (2) ) Distribution function along the crack front is written as
Wherein K I (1) Is a stress intensity factor distribution function under the action of a certain reference load (1);
(4) Introducing a macroscopic fundamental variation mode delta to the whole front of the crack c a s 0 (see also figure 2 of the drawings),
wherein delta c a is a variation of a characteristic crack length a, which is delta c a s 0 G(s) is a dimensionless spreading function;
(5) Introducing N local variation modes at N nodes (see figure 2)
Wherein the local variation function N j '(s) may be substituted with N in the formula (4) i (s) may be the same function or different functions.
(6) For the N local variation modes, listing N equations and calculating the integral of the right end of the equation to obtain the integral related to A i Is (1) is calculated by the following equation (7)
(7) Solving for the unknown coefficient A i Equation (7); then, the unknown quantity (stress intensity factor K) to be obtained can be obtained by using the following formulae (4) and (3) I (2) ) Distribution along the crack front.
(8) The self-consistency of the method, i.e. the condition that equation (1) also holds for the reference load itself, can be used directly from the original relatively coarse K by means of the program programmed according to step (1) and step (7) I (1) Calculating K corresponding to the reference load by approximate estimation value I (2) Then, a new precise reference load stress intensity factor distribution function K is obtained by using the following formula I
(9) The obtained new K I (1) General weight function (δ in equation (7)) c (…)/δ c a) And the surface force load,The volume force load and the temperature load are directly substituted into formula (7), and the equation set is solved again, so that the stress intensity factor distribution function K under the action of any surface force load, volume force load and temperature load can be obtained with high precision and high efficiency I (2) The numerical solution of (c).
For quadratic and above quadratic local variation function and basic interpolation type function N j (s) the total number of nodes should satisfy the requirements of the corresponding times, such as: for twice, N is odd number 2M +1; for L times, N is LM +1; wherein M is a positive integer.
Example 2
Referring to fig. 1, 2, 3, 4, 5 and 6, according to the method for determining the stress intensity factor distribution of the crack front edge of the structural member in example 1, the crack front edge stress intensity factor of the semi-elliptical surface crack in the flat plate is divided under thermal shock (thermal load)The cloth was determined. The lower graph shows a hemielliptic surface crack with a depth ratio a/w =0.5 and a morphic ratio a/c =0.5, at Θ 0 The time course of the stress intensity factor distribution of the crack front in the case of thermal shock of-300 ℃. Where M is a dimensionless stress intensity factor, fo is a dimensionless time, φ is the position of the crack front (parameter angle), and Bi is the heat exchange condition Biot number at impact. The distribution of the stress intensity factor along the crack front at 60 time points is determined. If the method is determined by using the existing direct elastomechanics method or the stress weight function method, 60 times of finite element analysis calculation and 60 times of stress intensity factor calculation are respectively needed. However, the technology of the invention is used for determination, so that only 1 time of general weight function calculation and 1 time of integral calculation are needed in total, and the total efficiency is improved by dozens of times; moreover, the accuracy is higher than in the previous methods. If further, the structural safety evaluation under 10 heat exchange conditions (Biot number) needs to be carried out, 600 times of finite element analysis calculation and 600 times of stress intensity factor calculation are respectively needed when the distribution of the stress intensity factor of the crack front is determined by using the existing elastic mechanics direct method or stress weight function method; the computational effort is so great that it is difficult to bear in engineering terms. However, the determination by the technology of the invention only needs 1 time of general weight function calculation and 10 times of integral calculation in total, can be completed in a short time, and the total calculation efficiency is higher.
The determination method of the stress intensity factor distribution of the crack front of the structural member under the action of the surface force load or the volume force load is similar to the embodiment.
Example 3
Referring to fig. 1, 2, 3, 4, 5, and 7, according to the method for determining the stress intensity factor distribution of the crack front edge of the structural member in example 1, the distribution of the stress intensity factor of the crack front edge of the axial semielliptical surface crack in the circular tube is determined when thermal shock (thermal load) and pressure shock (surface force load) simultaneously act (pressure-bearing thermal shock). The lower graph shows a depth ratio a/w =0.25, and an aspect ratio a/c =1/3 of axial semielliptical surface cracks, and the stress intensity factor distribution of the crack front edge changes along with time under the RanchoSeco pressure-bearing thermal shock condition. Wherein, K I For the stress intensity factor, t is the time and φ is the position of the crack front (parameter angle). The stress intensity factor distribution of the crack front at 81 time points was determined. The general weight function analysis is carried out on a PentiumIV/2.4GHz microcomputer, the 1417 seconds are used for the analysis, and the 678 seconds are used for the calculation of the integral. Since the amount of computational effort required to make determinations by other methods of the prior art is too large, no one has seen such detailed determination of the problem.
The determination method of the stress intensity factor distribution of the crack front edge of the structural member under the combined action of the surface force load and the volume force load, the combined action of the thermal load and the volume force load and the combined action of the three loads is similar to that of the embodiment.
Claims (5)
1. A method for determining stress intensity factor distribution of a structural member crack front edge mainly comprises the following steps: (1) Giving out the thermal load, the surface force load and the volume force load born by the structural member, and a general weight function method basic equation under the independent or combined action of the three loads, wherein the formula is as follows (1):
wherein the variation symbol delta c A first-order deviation score representing each physical quantity with respect to a crack position; u. u (1) 、t (1) And K I (1) Respectively is a displacement function, a boundary surface force function and an I-type stress intensity factor distribution function when any reference load acts; u. of *(2) 、t *(2) 、f *(2 )、Θ *(2) And K I (2) Respectively a boundary displacement function, a boundary surface force function, a volume force function, a temperature distribution function and an I-type stress intensity factor distribution function along the front edge of the crack under the action of the load to be solved; E. v, H and alpha are respectively the elastic modulus, poisson's ratio, equivalent elastic constant and coefficient of thermal expansion of the material; Γ is the crack front and s is the arc length along the crack front; sigma t 、∑ u Σ, and V are the face force known boundary, displacement known boundary, body boundary, and body volume, respectively; n is an external normal vector;
(2) Dividing the crack front edge into any N-1 subsegments by using N nodes, and introducing a basic interpolation function N at each node j j (s) and a local variation function N j '(s) which all satisfy the conditional formula (2):
(3) Will stress intensity factor K I (2) The distribution function along the crack front is expressed by the following equations (3) and (4):
wherein K is I (1) Is a stress intensity factor distribution function under the action of a certain reference load;
(4) Introducing a macroscopic fundamental variation mode delta to the whole crack front c a s 0 As shown in formula (5):
wherein, delta c a is a variation of a characteristic crack length a, which is delta c a s 0 G(s) is a dimensionless spread function;
(5) And introducing N local variation modes at N nodes, wherein the N local variation modes are as shown in a formula (6):
wherein N is j '(s) is a local variation function;
(6) For the N local variation modes, listing N equations and calculating the integral of the right end of the equation to obtain the integral related to A i The linear equation system of (1), equation (7):
(7) Solving for the unknown coefficient A i Equation (7); then, the stress intensity factor K is obtained by the following formulae (4) and (3) I (2) Distribution along the crack front;
(8) From K I (1) The approximate estimation value of (2) is calculated by the steps (1) to (7) to obtain K corresponding to the reference load I (2) Then, a new accurate reference load stress intensity factor distribution function K is obtained by using the following formula (8) I
(9) The obtained new K I (1) Precise solution of delta c (...)/δ c a, directly substituting the heat load, the surface force load and the volume force load into formula (7), solving the equation set again, and solving the stress intensity factor distribution function K under the action of any heat load, surface force load and volume force load I (2) The numerical solution of (c).
2. A method of determining the stress intensity factor distribution of a structural member crack front as claimed in claim 1, wherein: said basic interpolation type function N j (s) and a local variation function N j '(s) are taken as the same function.
3. A method of determining the stress intensity factor distribution of a structural member crack front as claimed in claim 1, wherein: said basic interpolation type function N j (s) and a local variation function N j '(s) are taken as different functions.
4. A method for determining the stress intensity factor distribution of the structural member crack front as claimed in claim 2 or 3, wherein: said basic interpolation type function N j (s) and a local variation function N j '(s), taking the linear mode as a linear function, requires N points.
5. A method for determining the stress intensity factor distribution of a structural member crack front as claimed in claim 2 or 3, wherein: said basic interpolation type function N j (s) and a local variation function N j '(s) is taken as an L-order function of the high-order mode, L is a natural number, L is more than or equal to 2, N = LM +1 points are needed, and M is a positive integer.
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| CN102063552B (en) * | 2011-01-07 | 2013-07-10 | 西安交通大学 | Method for determining rigidity of bolt connecting piece |
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