Structural thermal stress analysis method considering high-temperature accumulated damage

By establishing a database of high-temperature cumulative damage factor and finite element analysis, the problems of changes in thermal conductivity and mechanical bearing capacity of composite materials under long-term high-temperature cumulative action are solved, and effective prediction of structural force thermal load bearing capacity is achieved, with high calculation accuracy and wide application range.

CN119939992AActive Publication Date: 2025-05-06CHINA ACAD OF AEROSPACE AERODYNAMICS
View PDF 4 Cites 0 Cited by

Patent Information

Application Number
CN202411971562.0
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-12-30
Publication Date
2025-05-06
Estimated Expiration
2044-12-30

AI Technical Summary

Technical Problem

The prior art is difficult to effectively predict the changes in thermal conductivity and the decline in mechanical bearing capacity of composite materials under long-term high temperature accumulation, and lacks complete and effective numerical simulation methods.

Method used

By establishing a database of high-temperature cumulative damage factor, combined with finite element analysis, the damage accumulation process of the material's thermal conductivity, elastic modulus and strength at different working temperatures and time periods is taken into consideration, and the prediction of the thermal load carrying capacity of the structural force is achieved.

Benefits of technology

This method can consider the damage accumulation effect of materials at different working temperatures in detail, provide high calculation accuracy and wide application range of structural thermal stress analysis, and effectively predict the high-temperature accumulation damage process of the structure.

✦ Generated by Eureka AI based on patent content.

Smart Images

  • Figure CN119939992A_ABST
    Figure CN119939992A_ABST
Patent Text Reader

Abstract

The invention relates to a structural thermal stress analysis method considering high-temperature accumulated damage, and belongs to the field of structural thermal protection analys.The change of the material bearing capacity is described through high-temperature accumulated damage factors, and the high-temperature damage accumulation conditions of different part units under the action of thermal loads are given by combining finite element analysis; the high-temperature accumulated damage process of the thermal structure is directly simulated through iterative updating of material performance, and a structure thermal stress response analysis method under different force thermal bearing processes is given; the method is superior to a traditional thermal stress analysis method which only considers the current highest working temperature, the damage accumulation effects of the heat conductivity coefficient, the elastic modulus, the strength and the like of the material at the working temperatures at different moments are considered in detail, and the method has the advantages of being high in calculation precision and wide in application range.
Need to check novelty before this filing date? Find Prior Art

Description

Technical Field

[0001] The invention relates to a structural thermal stress analysis method considering high-temperature cumulative damage, and belongs to the field of structural thermal protection analysis. Background Art

[0002] Structural heat protection is one of the bottleneck technologies that restrict the improvement of aircraft performance. When an aircraft flies for a long time, its heat protection structure is subjected to long-term severe aerodynamic heat loads. The material may undergo significant physical and chemical changes when working in a high-temperature aerobic environment for a long time. Especially for composite materials, the pyrolysis, oxidation, ablation, etc. of the material will cause a significant decrease in the aircraft's carrying capacity. Under the effect of long-term high-temperature cumulative damage, the aircraft's heat protection bearing performance may fail, seriously threatening flight safety.

[0003] Currently, there are a variety of prediction methods for damage prediction of metal materials under mechanical loads. However, for the thermal structure analysis of a wider range of material components under combined mechanical and thermal loads, especially the changes in thermal conductivity and the decrease in mechanical bearing capacity of composite materials under the cumulative effect of long-term high temperature, most of them are simulated and evaluated by ground tests, which have long cycles and high costs, and there is still a lack of complete and effective numerical simulation methods. Summary of the invention

[0004] The problem to be solved by the present invention is to provide a structural thermal stress analysis method taking into account high-temperature cumulative damage. According to the damage accumulation process of the material thermal conductivity, elastic modulus and strength at different working temperatures and working times, a finite element structural thermal stress analysis method including high-temperature cumulative damage is established, and the structural damage evolution process and thermal stress flow considering the mechanical and thermal load loading history are given, which can realize the effective prediction of the mechanical and thermal load bearing capacity of the structure.

[0005] The technical solution of the present invention is as follows:

[0006] A structural thermal stress analysis method considering high temperature cumulative damage, comprising:

[0007] S1. According to the thermal conductivity, elastic modulus and material strength of the structural parts at different working temperatures and working times, a high-temperature cumulative damage factor database is established, where the high-temperature cumulative damage factor is expressed as f i =f i (T, t), i represents thermal conductivity, elastic modulus or material strength, T is the current working temperature, and t is the working time;

[0008] S2. Establish the initial finite element model of the structural parts before mechanical and thermal loading;

[0009] S3, applying the mechanical and thermal load environment conditions at the j-th load step to the structural parts, and solving the structural temperature field and thermal stress field at the j-th load step; the structural temperature field includes the current working temperature Tj , the current load step duration is expressed as Δt j , the jth load step is represented by t = t j , j = 1, 2, 3...;

[0010] S4, looping the mesh units of the finite element initial model, and obtaining the mesh unit high temperature cumulative damage factor increment according to the structural temperature field and thermal stress field at the j-th load step and the high temperature cumulative damage factor database established in step S1;

[0011] S5. updating the high temperature cumulative damage factor of the grid unit according to the increment of the high temperature cumulative damage factor of the grid unit;

[0012] S6. Calculate the thermal conductivity, elastic modulus and material strength of the updated grid unit according to the high-temperature cumulative damage factor of the updated grid unit;

[0013] S7, comparing the thermal stress of the grid unit in step S3 and the material strength of the updated grid unit in step S6, to determine whether the grid unit is completely destroyed;

[0014] S8, applying the mechanical and thermal load environment conditions at the next load step, solving the structural temperature field and thermal stress field at the next load step, and returning to step S4;

[0015] S9, until the structural parts can no longer bear mechanical loads.

[0016] In the above-mentioned structural thermal stress analysis method considering high temperature cumulative damage, the initial high temperature cumulative damage factor value of the finite element initial model established in step S2 is set to zero, that is, f i (T0, t0)=0.

[0017] In the above-mentioned structural thermal stress analysis method considering high temperature cumulative damage, the increment of the high temperature cumulative damage factor of the grid unit obtained in step S4 is expressed as Δf i (T j ,Δt j ), where T j is the temperature at the current j-th load step, Δt j is the time step of the current j-th load step, and i is the thermal conductivity, elastic modulus or material strength.

[0018] In the above-mentioned structural thermal stress analysis method considering high temperature cumulative damage, the step S5 updates the high temperature cumulative damage factor of the grid unit according to the increment of the high temperature cumulative damage factor of the grid unit, including:

[0019] f i (T j+1 ,t j+1 )=fi (T j ,t j )+Δf(T j ,Δt j )

[0020] Among them, f i (T j+1 ,t j+1 ) represents the high temperature cumulative damage factor of the unit at the next moment, i.e., the j+1th load step, f i (T j ,t j ) represents the high temperature cumulative damage factor of the unit at the current moment, i.e., the jth load step.

[0021] In the above-mentioned structural thermal stress analysis method considering high temperature cumulative damage, the step S6 calculates the updated unit thermal conductivity, elastic modulus and material strength according to the updated unit high temperature cumulative damage factor, including:

[0022] k j+1 =k*(1-f k (T j+1 ,t j+1 )),

[0023] E j+1 =E*(1-f E (T j+1 ,t j+1 )),

[0024] S j+1 =S*(1-f S (T j+1 ,t j+1 ))

[0025] Among them, k j+1 is the updated unit thermal conductivity, E j+1 is the updated unit elastic modulus, S j+1 is the updated unit material strength, k is the initial thermal conductivity, E is the initial elastic modulus, and S is the initial material strength.

[0026] In the above-mentioned structural thermal stress analysis method considering high temperature cumulative damage, in step S7, if the thermal stress>material strength, it is judged that the grid unit is completely destroyed and the unit elastic modulus takes a minimum value; otherwise, it is judged that the grid unit is not destroyed.

[0027] A structural thermal stress analysis system considering high temperature cumulative damage, comprising:

[0028] The database establishment module establishes a high-temperature cumulative damage factor database based on the thermal conductivity, elastic modulus and material strength of the structural parts at different working temperatures and working times, where the high-temperature cumulative damage factor is expressed as f i =f i (T, t), i represents thermal conductivity, elastic modulus or material strength, T is the current working temperature, and t is the working time;

[0029] Model building module, to build the initial finite element model of the structural parts before mechanical and thermal loading;

[0030] The first calculation module applies the mechanical and thermal load environment conditions at the j-th load step to the structural member, and solves the structural temperature field and thermal stress field at the j-th load step; the structural temperature field includes the current working temperature T j , the current load step duration is expressed as Δt j , the jth load step is represented by t = t j , j = 1, 2, 3...;

[0031] The second calculation module cycles the mesh units of the finite element initial model, and obtains the mesh unit high temperature cumulative damage factor increment according to the structural temperature field and thermal stress field at the j-th load step and the high temperature cumulative damage factor database established in step S1;

[0032] An updating module, which updates the high temperature cumulative damage factor of the grid unit according to the increment of the high temperature cumulative damage factor of the grid unit;

[0033] A third calculation module calculates the thermal conductivity, elastic modulus and material strength of the updated grid unit according to the high-temperature cumulative damage factor of the updated grid unit;

[0034] The comparison module compares the thermal stress of the grid unit and the material strength of the updated grid unit to determine whether the grid unit has reached complete destruction.

[0035] A computer device comprises a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the above method.

[0036] A computer program product comprises a computer program, which implements the steps of the above method when executed by a processor.

[0037] Compared with the prior art, the present invention has at least the following beneficial effects:

[0038] (1) The structural thermal stress analysis method provided by the embodiment of the present invention describes the change of the material's bearing capacity through the high-temperature cumulative damage factor according to the damage accumulation process of the material under high temperature for a long time, and combines finite element analysis to give the high-temperature damage accumulation of units in different parts under the action of thermal loads. The high-temperature cumulative damage process of the thermal structure is directly simulated through iterative updating of material properties, and a structural thermal stress response analysis method under different thermal load histories is given. The method is superior to the traditional thermal stress analysis method that only considers the current maximum working temperature. The present invention considers in detail the damage accumulation effects of the material thermal conductivity, elastic modulus and strength at different working temperatures, and has the characteristics of high calculation accuracy and wide application range.

[0039] (2) The structural thermal stress analysis method provided in the embodiment of the present invention comprehensively considers the influence of different working temperatures and working hours of the material, and reflects the cumulative effect of high temperature damage;

[0040] (3) The structural thermal stress analysis method provided by the embodiment of the present invention comprehensively considers the influence of high temperature cumulative damage on thermal conductivity, elastic modulus and strength data, covers the main performance parameters of heat transfer and load-bearing, and describes the influence of high temperature cumulative damage more precisely and accurately;

[0041] (4) The structural thermal stress analysis method provided by the embodiment of the present invention provides the structural damage evolution process and thermal stress process considering the mechanical and thermal load loading history, which can realize the effective prediction of the mechanical and thermal load bearing capacity of the structure;

[0042] (5) The structural thermal stress analysis method provided in the embodiment of the present invention considers in detail the damage accumulation effect of the material thermal conductivity, elastic modulus and strength at different working temperatures, and has the characteristics of high calculation accuracy and wide application range. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 This is a flow chart of a method for analyzing structural thermal stress considering high-temperature cumulative damage in an embodiment of the present invention. DETAILED DESCRIPTION

[0044] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0045] like Figure 1 As shown, the structural thermal stress analysis method considering high temperature cumulative damage provided by the embodiment of the present invention specifically includes the following steps:

[0046] S1. According to the thermal conductivity, elastic modulus and material strength of the structural parts at different working temperatures and working times, a high-temperature cumulative damage factor database is established, where the high-temperature cumulative damage factor is expressed as f i =f i(T, t), i = k represents thermal conductivity, i = E represents elastic modulus, i = S represents material strength, T is the current working temperature, and t is the working time;

[0047] S2. Establish the initial finite element model of the structural component before mechanical and thermal loading; the initial high temperature cumulative damage value is set to zero, f(T0, t0) = 0;

[0048] S3, apply the mechanical and thermal load environment conditions at the j-th load step to the structural parts, and solve the structural temperature field and thermal stress field at the j-th load step; the structural temperature field includes the current working temperature T j and the current load step duration Δt j , the jth load step is represented by t = t j ;

[0049] S4, looping the mesh units of the finite element initial model, and obtaining the mesh unit high temperature cumulative damage factor increment represented by Δf according to the structural temperature field and thermal stress field at the j-th load step and the high temperature cumulative damage factor database established in step S1. i (T j ,Δt j ), where T j is the temperature of the current load step, Δt j is the cumulative time of the current load step, i is the thermal conductivity, elastic modulus or material strength;

[0050] S5. According to the increment of the high temperature cumulative damage factor of the grid unit, the high temperature cumulative damage factor of the grid unit is updated, including:

[0051] f i (T j+1 ,t j+1 )=f i (T j ,t j )+Δf(T j ,Δt j )

[0052] Among them, f i (T j+1 ,t j+1 ) represents the high temperature cumulative damage factor of the unit at the next moment, i.e., the j+1th load step, f i (T j ,t j ) represents the high temperature cumulative damage factor of the unit at the current moment, i.e., the jth load step.

[0053] S6. Calculate the thermal conductivity, elastic modulus and material strength of the updated grid unit according to the updated high temperature cumulative damage factor of the grid unit, including:

[0054] kj+1 =k*(1-f k (T j+1 ,t j+1 )),

[0055] E j+1 =E*(1-f E (T j+1 ,t j+1 )),

[0056] S j+1 =S*(1-f S (T j+1 ,t j+1 ))

[0057] Among them, k j+1 is the updated unit thermal conductivity, E j+1 is the updated unit elastic modulus, S j+1 is the updated unit material strength, k is the initial thermal conductivity, E is the initial elastic modulus, and S is the initial material strength.

[0058] S7, comparing the thermal stress of the grid unit in step S3 and the material strength of the updated grid unit in step S6, to determine whether the grid unit is completely destroyed; if the thermal stress is greater than the material strength, the grid unit is determined to be completely destroyed, the unit elastic modulus takes a minimum value, and the process proceeds to step S8; otherwise, the grid unit is determined to be undestroyed, and the process proceeds to step S8;

[0059] S8, applying the mechanical and thermal load environment conditions at the next load step, solving the structural temperature field and thermal stress field at the next load step, and returning to step S4;

[0060] S9, until the structural parts can no longer bear mechanical loads.

[0061] The embodiment of the present invention takes into account the structural thermal stress analysis method of high temperature cumulative damage, defines a high temperature cumulative damage factor to describe the performance changes of the thermal conductivity, elastic modulus and strength of the material at different working temperatures and different working durations, and uses it as the material performance input condition for the structural temperature field and thermal stress analysis. Based on the finite element method, the high temperature cumulative damage factor of each unit is calculated in real time according to the unit temperature and thermal stress state during thermal loading, and the thermal conductivity, elastic modulus and strength performance of the unit material are updated in real time. Through iterative calculation, the heat conduction and thermal stress re-balance state after local high temperature cumulative damage can be simulated, thereby realizing a structural thermal stress analysis method taking into account high temperature cumulative damage.

[0062] The present invention also provides a structural thermal stress analysis system considering high temperature cumulative damage, comprising:

[0063] The database establishment module establishes a high-temperature cumulative damage factor database based on the thermal conductivity, elastic modulus and material strength of the structural parts at different working temperatures and working times, where the high-temperature cumulative damage factor is expressed as f i =f i (T, t), i represents thermal conductivity, elastic modulus or material strength, T is the current working temperature, and t is the working time;

[0064] Model building module, to build the initial finite element model of the structural parts before mechanical and thermal loading;

[0065] The first calculation module applies the mechanical and thermal load environment conditions at the j-th load step to the structural member, and solves the structural temperature field and thermal stress field at the j-th load step; the structural temperature field includes the current working temperature T j , the current load step duration is expressed as Δt j , the jth load step is represented by t = t j , j = 1, 2, 3...;

[0066] The second calculation module cycles the mesh units of the finite element initial model, and obtains the mesh unit high temperature cumulative damage factor increment according to the structural temperature field and thermal stress field at the j-th load step and the high temperature cumulative damage factor database established in step S1;

[0067] An updating module, which updates the high temperature cumulative damage factor of the grid unit according to the increment of the high temperature cumulative damage factor of the grid unit;

[0068] A third calculation module calculates the thermal conductivity, elastic modulus and material strength of the updated grid unit according to the high-temperature cumulative damage factor of the updated grid unit;

[0069] The comparison module compares the thermal stress of the grid unit and the material strength of the updated grid unit to determine whether the grid unit has reached complete destruction.

[0070] The present invention also provides a computer device, comprising a memory, a processor and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the above method.

[0071] The present invention also provides a computer program product, comprising a computer program, which implements the steps of the above method when executed by a processor.

[0072] The embodiment of the present invention describes the change of the material's bearing capacity through the high-temperature cumulative damage factor according to the damage accumulation process of the material under high temperature for a long time, and combines finite element analysis to give the high-temperature damage accumulation of units in different parts under thermal loads. It directly simulates the high-temperature cumulative damage process of the thermal structure through iterative updates of material properties, and gives a method for analyzing the thermal stress response of the structure under different thermal load histories. It is superior to the traditional thermal stress analysis method that only considers the current maximum operating temperature. The embodiment of the present invention considers in detail the damage accumulation effects of the material's thermal conductivity, elastic modulus, and strength at different operating temperatures, and has the characteristics of high calculation accuracy and a wide range of applications.

[0073] The structural thermal stress analysis method considering high temperature cumulative damage provided by the embodiment of the present invention comprehensively considers the influence of different working temperatures and working hours of the material, and reflects the cumulative effect of high temperature damage; comprehensively considers the influence of thermal conductivity, elastic modulus and strength data on high temperature cumulative damage, and covers the main performance parameters of heat transfer and load-bearing; for different material properties such as thermal conductivity, elastic modulus and strength data, corresponding high temperature cumulative damage factors f are established respectively. i =f i (T, t), i=k represents thermal conductivity, i=E represents elastic modulus, i=S represents material strength, T is the current working temperature, and t is the current cumulative time. The description of the impact of high temperature cumulative damage is more detailed and accurate.

[0074] In the embodiment of the present invention, the high-temperature cumulative damage factor calculation method at different times is based on the difference in mechanical and thermal responses of different parts of the thermal structure, that is, different parts have different temperature fields and stress lengths. Therefore, the high-temperature cumulative damage factor is calculated for each unit, and the damage extension process is more precisely described; for the unit temperature field and thermal stress field under each load step increment, the unit high-temperature cumulative damage factor increment Δf is extracted and calculated respectively. i (T j ,t j ) and accumulate them, j represents the number of load steps, realizing the evolution and superposition of high temperature damage factors over time.

[0075] The above description is only the best specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

[0076] The contents not described in detail in the specification of the present invention belong to the common knowledge of the professionals in this field.

Claims

1. A structural thermal stress analysis method considering high temperature cumulative damage, characterized in that: include: S1. According to the thermal conductivity, elastic modulus and material strength of the structural parts at different working temperatures and working times, a high-temperature cumulative damage factor database is established, where the high-temperature cumulative damage factor is expressed as f i =f i (T, t), i represents thermal conductivity, elastic modulus or material strength, T is the current working temperature, and t is the working time; S2. Establish the initial finite element model of the structural parts before mechanical and thermal loading; S3, applying the mechanical and thermal load environment conditions at the j-th load step to the structural parts, and solving the structural temperature field and thermal stress field at the j-th load step; the structural temperature field includes the current working temperature T j , the current load step duration is expressed as Δt j , the jth load step is represented by t = t j , j = 1, 2, 3...; S4, looping the mesh units of the finite element initial model, and obtaining the mesh unit high temperature cumulative damage factor increment according to the structural temperature field and thermal stress field at the j-th load step and the high temperature cumulative damage factor database established in step S1; S5. updating the high temperature cumulative damage factor of the grid unit according to the increment of the high temperature cumulative damage factor of the grid unit; S6. Calculate the thermal conductivity, elastic modulus and material strength of the updated grid unit according to the high-temperature cumulative damage factor of the updated grid unit; S7, comparing the thermal stress of the grid unit in step S3 and the material strength of the updated grid unit in step S6, to determine whether the grid unit is completely destroyed; S8, applying the mechanical and thermal load environment conditions at the next load step, solving the structural temperature field and thermal stress field at the next load step, and returning to step S4; S9, until the structural parts can no longer bear mechanical loads.

2. The structural thermal stress analysis method considering high temperature cumulative damage according to claim 1 is characterized in that: The initial high temperature cumulative damage factor value of the finite element initial model established in step S2 is set to zero, that is, f i (T0, t0)=0.

3. The structural thermal stress analysis method considering high temperature cumulative damage according to claim 1 is characterized in that: The increment of the high temperature cumulative damage factor of the grid unit obtained in step S4 is expressed as Δf i (T j ,Δt j ), where T j is the temperature at the current j-th load step, Δt j is the time step of the current j-th load step, and i is the thermal conductivity, elastic modulus or material strength.

4. The structural thermal stress analysis method considering high temperature cumulative damage according to claim 3 is characterized in that: In step S5, the high temperature cumulative damage factor of the grid unit is updated according to the increment of the high temperature cumulative damage factor of the grid unit, including: f i (T j+1 ,t j+1 )=f i (T j ,t j )+Δf(T j ,Δt j ) Among them, f i (T j+1 ,t j+1 ) represents the high temperature cumulative damage factor of the unit at the next moment, i.e., the j+1th load step, f i (T j ,t j ) represents the high temperature cumulative damage factor of the unit at the current moment, i.e., the jth load step.

5. The structural thermal stress analysis method considering high temperature cumulative damage according to claim 1, characterized in that: The step S6 calculates the updated unit thermal conductivity, elastic modulus and material strength according to the updated unit high temperature cumulative damage factor, including: k j+1 =k*(1-f k (T j+1 ,t j+1 )), E j+1 =E*(1-f E (T j+1 ,t j+1 )), S j+1 =S*(1-f S (T j+1 ,t j+1 )) Among them, k j+1 is the updated unit thermal conductivity, E j+1 is the updated unit elastic modulus, S j+1 is the updated unit material strength, k is the initial thermal conductivity, E is the initial elastic modulus, and S is the initial material strength.

6. The structural thermal stress analysis method considering high temperature cumulative damage according to claim 1 is characterized in that: In step S7, if the thermal stress is greater than the material strength, the grid unit is judged to be completely destroyed and the unit elastic modulus takes a minimum value; otherwise, the grid unit is judged to be not destroyed.

7. A structural thermal stress analysis system considering high temperature cumulative damage, characterized in that: include: The database establishment module establishes a high-temperature cumulative damage factor database based on the thermal conductivity, elastic modulus and material strength of the structural parts at different working temperatures and working times, where the high-temperature cumulative damage factor is expressed as f i =f i (T, t), i represents thermal conductivity, elastic modulus or material strength, T is the current working temperature, and t is the working time; Model building module, to build the initial finite element model of the structural parts before mechanical and thermal loading; The first calculation module applies the mechanical and thermal load environment conditions at the j-th load step to the structural member, and solves the structural temperature field and thermal stress field at the j-th load step; the structural temperature field includes the current working temperature T j , the current load step duration is expressed as Δt j , the jth load step is represented by t = t j , j = 1, 2, 3...; The second calculation module cycles the mesh units of the finite element initial model, and obtains the mesh unit high temperature cumulative damage factor increment according to the structural temperature field and thermal stress field at the j-th load step and the high temperature cumulative damage factor database established in step S1; An updating module, which updates the high temperature cumulative damage factor of the grid unit according to the increment of the high temperature cumulative damage factor of the grid unit; A third calculation module calculates the thermal conductivity, elastic modulus and material strength of the updated grid unit according to the high-temperature cumulative damage factor of the updated grid unit; The comparison module compares the thermal stress of the grid unit and the material strength of the updated grid unit to determine whether the grid unit has reached complete destruction.

8. A computer device comprising a memory, a processor and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method of claim 1.

9. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to claim 1 are implemented.

Citation Information

Patent Citations

  • Time-dependent local stress-strain method and tool software for analyzing strength and service life of high-temperature structure

    CN114698393A

  • Method for calculating fatigue life of metal material under spectral load

    CN115310311A

  • Rock mass high temperature-aging-elastoplastic coupling damage calculation method

    CN118607315A

  • Method for designing lifetime of weld zone of high-temperature apparatus

    JP2009162647A