WO2022077204A1 - 高温结构强度和寿命分析的时间相关局部应力应变方法及工具软件 - Google Patents
高温结构强度和寿命分析的时间相关局部应力应变方法及工具软件 Download PDFInfo
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- the invention relates to the technical field of computer simulation, and more particularly, to a computer simulation technology for high-temperature structural strength and life analysis.
- the development of a new generation of advanced ultra-supercritical steam turbine unit technology has become an important issue faced by domestic thermal power, nuclear power and other industries.
- advanced energy equipment a large number of engineering components face extreme operating conditions such as high temperature and high pressure.
- the intermediate heat exchanger support in the fast reactor nuclear power system has a normal operating temperature of 540°C and a temperature of 610°C under transient conditions, which both exceed the creep initiation temperature of the corresponding material 316H stainless steel. Therefore, the problem of creep deformation and fracture is the failure mode that needs to be focused on in the strength design and safety evaluation of nuclear power high-temperature structures.
- the stress-strain response of the structure under creep behavior can be calculated according to the creep constitutive equation.
- the geometric structure of actual components often has many discontinuous areas such as openings, chamfers, etc., and there are significant stress and strain concentrations in this area.
- the accurate calculation of the creep stress-strain behavior of the dangerous point in this area is an important part of the structural integrity evaluation.
- Existing time-independent local stress-strain methods (such as the Neuber method) cannot describe the time-dependent creep behavior of high-temperature structures.
- Some researchers extend the Neuber equation to predict the stress-strain response of high-temperature structures, which usually leads to certain errors.
- Precise stress-strain methods namely time-dependent local stress-strain methods, are an important topic in the field of structural integrity.
- a time-dependent local stress-strain method for high-temperature structural strength and life analysis is proposed, the method is aimed at a load component under high temperature conditions, the load component has a structural discontinuity area, and the method includes: :
- the step of obtaining working condition parameters include design temperature, design load, total dwell time, material of the component and structural danger point of the component, and the structural danger point of the component is related to the structural discontinuity area;
- the material parameters include the material's creep constitutive equation, elastic modulus, Poisson's ratio, stress-strain relationship curve and equivalent elastic modulus, and establish a finite element model according to the material parameters and working condition parameters;
- the elastic-plastic analysis step the elastic-plastic analysis is performed based on the finite element model, and the initial equivalent stress, the initial equivalent strain and the initial stress of the far-field area of the structural danger point of the component are determined;
- limit analysis is performed based on the finite element model to determine the limit load and the initial reference stress of the structural danger point;
- the elastic analysis is performed based on the finite element model, and the elastic stress, elastic strain and stress concentration factor of the dangerous point of the structure are determined;
- the boundary condition setting step is to set the boundary conditions of the iterative operation.
- the boundary conditions include: total holding time, total time, maximum allowable stress drop and time step;
- each iteration step the displacement control intermediate variable and the load control intermediate variable are calculated, and the result variable of each iteration step is calculated based on the displacement control intermediate variable and the load control intermediate variable: stress drop;
- the relationship between the local stress and strain of the structural danger point of the component and time is determined according to the calculation results output by each iteration step.
- Material parameters are obtained by querying the material properties library:
- the material is tested by a static method or a dynamic thermomechanical analyzer to obtain the elastic modulus E and Poisson's ratio v at the design temperature T,
- a round bar tensile test at the design temperature T is performed on the material to obtain the plastic elongation strength of the material, and the stress-strain relationship curve of the material is obtained according to the plastic elongation strength.
- the limit load PL is obtained by performing limit analysis based on the finite element model, and the initial reference stress of the structural danger point is calculated according to the limit load
- the elastic stress ⁇ elastic and elastic strain ⁇ elastic of the structural dangerous point are determined by performing elastic analysis based on the finite element model, and then the stress concentration factor K t of the structural dangerous point is calculated;
- E is the elastic modulus
- ⁇ ref is the initial reference stress at the dangerous point of the structure.
- the displacement control intermediate variables include: a creep strain increment, a far-field creep increment, a reference stress drop, a far-field elastic strain increment, and a reference strain increment;
- A is the creep constitutive parameter
- E is the elastic modulus
- ⁇ t is the time step
- ⁇ t is the time step, is the initial stress
- the load control intermediate variables include: a creep strain increment and a reference strain increment;
- A is the creep constitutive parameter and ⁇ t is the time step.
- K is the stress concentration factor
- ⁇ c is the creep strain
- ⁇ is the equivalent strain
- ⁇ is the stress.
- the calculation result of the iterative step is output: total stress ⁇ i , total strain ⁇ i , reference stress Reference strain far field stress and the total holding time t i ,
- the total stress ⁇ i is calculated as follows:
- ⁇ i ⁇ i-1 + ⁇ i ;
- the total strain ⁇ i is calculated as follows:
- the total holding time t i is calculated as follows:
- the structural hazard points are selected from the structural discontinuities based on the stress field.
- a time-dependent local stress-strain tool software for high temperature structural strength and life analysis is proposed.
- the tool software is based on finite element software, and the tool software is aimed at load components under high temperature conditions.
- the load component has a structural discontinuity area, and the tool software includes: a parameter acquisition component, a finite element modeling and operation component, an iterative operation component and a result display component.
- the parameter acquisition component acquires working condition parameters and material parameters, and the working condition parameters include design temperature, design load, total dwell time, material of the component, and structural danger point of the component, and the structural danger point of the component is related to the structural discontinuity area;
- Material parameters include the material's creep constitutive equation, elastic modulus, Poisson's ratio, stress-strain relationship curve, and equivalent elastic modulus.
- Finite element modeling and calculation components establish a finite element model according to material parameters; perform elastic-plastic analysis based on the finite element model, and determine the initial equivalent stress, initial equivalent strain and initial stress of the far-field area at the structural danger point of the component; based on the finite element model
- the limit analysis is performed on the element model to determine the limit load and the initial reference stress of the structural danger point; the elastic analysis is performed based on the finite element model to determine the elastic stress, elastic strain and stress concentration factor of the structural danger point.
- the iterative operation component sets the boundary conditions of the iterative operation.
- the boundary conditions include: total holding time, total time, maximum allowable stress drop and time step; the iterative operation component executes the iterative operation steps, and in each iteration step, calculates the displacement control intermediate variable and load-controlled intermediate variables, calculate the resulting variable for each iteration step based on the displacement-controlled intermediate variables and the load-controlled intermediate variables: stress drop; compare the stress drop with the maximum allowable stress drop, and adjust the time if the stress drop is greater than the maximum allowable stress drop
- the intermediate and result variables of the iteration step are recalculated; if the stress drop is not greater than the maximum allowable stress drop, the calculation results of the iteration step are output: total stress, total strain, reference stress, reference strain, far-field stress and Total holding time; judge whether the calculation time reaches the total time, if the total time is reached, the iteration step ends; if the total time is not reached, the next iteration step is entered.
- the result display component generates a dual vertical axis chart of strain/stress versus time according to the calculation results output by each iteration step, and displays the relationship between the local stress-strain and time at the structural danger points of the component.
- the time-dependent local stress-strain method and tool software for high-temperature structural strength and life analysis proposed by the present invention aim at the problem of stress-strain prediction in the local area of components, and based on the stress-strain distribution characteristics of components, the traditional differential Neuber formula is modified, and an improved method is proposed. Local stress-strain calculation method.
- the method and tool software simultaneously solve the problem of stress-strain prediction in local areas of components under load control or displacement control.
- FIG. 1 discloses a flow chart of a time-dependent local stress-strain method for high temperature structural strength and life analysis according to an embodiment of the present invention.
- a load member which is a simplified bolt member, in a specific example of a time-dependent local stress-strain method for high temperature structural strength and life analysis according to an embodiment of the present invention.
- FIG. 3 discloses the creep stress-strain behavior at structural critical points of the simplified bolted component of the example shown in FIG. 2 .
- FIG. 4 discloses a structural block diagram of time-dependent local stress-strain tool software for high-temperature structural strength and life analysis according to an embodiment of the present invention.
- the present invention proposes a time-dependent high-temperature structural strength and life analysis Local stress-strain method for load-bearing components with regions of structural discontinuity under high temperature conditions.
- the method includes:
- the operating parameters include the design temperature, the design load, the total dwell time, the material of the component, and the structural hazard point of the component, where the structural hazard point of the component is related to the structural discontinuity area.
- the structural hazard points are selected from the structural discontinuities based on the stress field.
- Material parameters include the material's creep constitutive equation, elastic modulus, Poisson's ratio, stress-strain relationship curve and equivalent elastic modulus, and a finite element model is established based on material parameters and working condition parameters.
- material parameters include the material's creep constitutive equation, elastic modulus, Poisson's ratio, stress-strain relationship curve and equivalent elastic modulus, and a finite element model is established based on material parameters and working condition parameters.
- the material parameters are obtained by querying a material property library:
- the stress-strain relationship curve of the material under the design temperature T condition is obtained.
- the material parameters can be obtained experimentally:
- the material is tested by a static method or a dynamic thermomechanical analyzer to obtain the elastic modulus E and Poisson's ratio v at the design temperature T.
- Either the static method test or the dynamic thermomechanical analyzer test can be used to obtain the elastic modulus E and Poisson's ratio v,
- the material is subjected to a round bar tensile test at the design temperature T to obtain the plastic elongation strength of the material, and the stress-strain relationship curve of the material is obtained according to the plastic elongation strength.
- a finite element model will be established according to material parameters and working condition parameters.
- building the finite element model uses engineering simulation finite element software.
- finite element software mainly for structural mechanics analysis, such as Abaqus, Ansys, etc.
- the elastic-plastic analysis is carried out based on the finite element model, and the initial equivalent stress, initial equivalent strain and initial stress of the far-field region of the structural danger point of the component are determined.
- limit analysis step Perform limit analysis based on the finite element model to determine the limit load and initial reference stress at the structural hazard point.
- the limit load PL is obtained by performing limit analysis based on the finite element model, and the initial reference stress of the structural danger point is calculated according to the limit load
- the elastic analysis step The elastic analysis is carried out based on the finite element model, and the elastic stress, elastic strain and stress concentration factor of the dangerous point of the structure are determined.
- the elastic stress ⁇ elastic and elastic strain ⁇ elastic of the structural dangerous point are determined by performing elastic analysis based on the finite element model, and then the stress concentration factor K t of the structural dangerous point is calculated;
- E is the elastic modulus
- ⁇ ref is the initial reference stress at the dangerous point of the structure.
- the boundary conditions include: total dwell time, total time, maximum allowable stress drop, and time step.
- each iteration step the displacement control intermediate variable and the load control intermediate variable are calculated, and the result variable of each iteration step is calculated based on the displacement control intermediate variable and the load control intermediate variable: stress drop;
- the displacement control intermediate variables include: a creep strain increment, a far-field creep increment, a reference stress drop, a far-field elastic strain increment, and a reference strain increment;
- A is the creep constitutive parameter
- E is the elastic modulus
- ⁇ t is the time step
- ⁇ t is the time step, is the initial stress
- the load control intermediate variables include: a creep strain increment and a reference strain increment;
- A is the creep constitutive parameter and ⁇ t is the time step.
- K is the stress concentration factor
- ⁇ c is the creep strain
- ⁇ is the equivalent strain
- ⁇ is the stress.
- the calculation result of the iterative step is output: total stress ⁇ i , total strain ⁇ i , reference stress Reference strain far field stress and the total holding time t i ,
- the total stress ⁇ i is calculated as follows:
- ⁇ i ⁇ i-1 + ⁇ i ;
- the total strain ⁇ i is calculated as follows:
- the total holding time t i is calculated as follows:
- FIG. 1 discloses a flow chart of a time-dependent local stress-strain method for high temperature structural strength and life analysis according to an embodiment of the present invention. Referring to Figure 1, the method of this embodiment includes the following steps:
- the working condition parameters include: design temperature T, design load P, design total holding time t total , specific materials and structural dimensions of high-temperature structures or components.
- the material parameters include: creep constitutive equation (taking Norton constitutive equation as an example, see the following formula), elastic modulus E, Poisson's ratio v, stress-strain relationship curve and equivalent elastic modulus
- n is the stress index parameter in the creep constitutive equation.
- Material parameters can be obtained by querying the material property library, and material parameters can also be obtained through experiments. If the material parameters are obtained by experiment, the elastic modulus E and Poisson's ratio v can be obtained by static method test or dynamic thermomechanical analyzer test.
- the creep constitutive equation can be obtained by the round bar tensile creep test.
- the stress-strain relationship curve can be obtained by round bar tensile test.
- P is the design load
- PL is the ultimate load
- ⁇ y is the yield strength, which is the stress corresponding to 0.2% plastic deformation.
- E is the elastic modulus
- ⁇ ref is the initial reference stress at the dangerous point of the structure.
- time step ⁇ t the parameters required for the analysis: time step ⁇ t, total holding time t total , maximum allowable stress drop ⁇ allow per step.
- the time step ⁇ t, the total holding time t total , and the maximum allowable stress drop ⁇ allow per step are the boundary conditions of the iterative operation.
- S111 Determine whether the holding time t i corresponding to the iteration step i is greater than or equal to the total holding time t total ; if it is satisfied, stop the iterative calculation, otherwise, perform the i+1th step iterative calculation.
- the load component is a bolt component. It is now necessary to obtain the stress-strain response of the root of the thread under creep conditions for the bolt assembly.
- the bolt design temperature is 538°C
- the design displacement load is 0.171mm
- the design life is 30,000 hours
- the component material is 316 stainless steel.
- Figure 2 reveals the simplified modeling model of the bolt component, that is, in this example, the load component is a simplified bolt part.
- Step 1 Obtain the design condition parameters.
- the bolt design temperature T is 538°C
- the design displacement load is 0.171mm
- the design life t total is 30,000 hours
- the component material is 316 stainless steel
- the structural dimensions are shown in Figure 2: bolt diameter 20mm, thread diameter 18mm, thread length 0.73 mm
- the inclination angle of the transition slope between the thread and the bolt is 15 degrees.
- Step 2 Obtain material property data.
- the elastic modulus E at 538°C was 164 GPa and the Poisson's ratio v was 0.3 by the static method.
- a round bar tensile test was carried out at 538°C, and the 0.2% plastic elongation strength R P0.2 was 136MPa.
- a high temperature round bar tensile creep test at 538°C was carried out, and the creep constitutive equation was obtained from the test
- Step 6 Write an iterative calculation program according to the aforementioned S107 - S111 , input the above parameters into the iterative calculation program, and carry out the iterative calculation.
- FIG. 3 discloses the creep stress-strain behavior at structural critical points of the simplified bolted component of the example shown in FIG. 2 .
- Figure 3 is a double-axis coordinate graph, the abscissa is the creep holding time, the unit is hours.
- the left ordinate is the stress, in the illustrated embodiment, the von-Mises stress, in Mpa.
- the right ordinate is the equivalent strain.
- the solid-line curve in Fig. 3 represents stress, and the dashed-line curve represents strain.
- the invention also provides a time-dependent local stress-strain tool software for high-temperature structural strength and life analysis.
- FIG. 4 discloses a structural block diagram of time-dependent local stress-strain tool software for high-temperature structural strength and life analysis according to an embodiment of the present invention.
- the tool software is based on finite element software, which is aimed at load parts under high temperature conditions, and the load parts have structural discontinuities.
- the tool software includes: a parameter acquisition component 201 , a finite element modeling and operation component 202 , an iterative operation component 203 and a result display component 204 .
- the parameter acquisition component 201 acquires working condition parameters and material parameters.
- the working condition parameters include design temperature, design load, total dwell time, material of the component, and structural danger point of the component, which is related to the structural discontinuity area.
- Material parameters include the material's creep constitutive equation, elastic modulus, Poisson's ratio, stress-strain relationship curve, and equivalent elastic modulus.
- the finite element modeling and calculation component 202 establishes a finite element model according to material parameters; performs elastic-plastic analysis based on the finite element model, and determines the initial equivalent stress, initial equivalent strain and initial stress of the far-field region of the structural danger point of the component; based on the finite element model
- the limit analysis is performed on the element model to determine the limit load and the initial reference stress of the structural danger point
- the elastic analysis is performed based on the finite element model to determine the elastic stress, elastic strain and stress concentration factor of the structural danger point.
- the finite element modeling and computing component 202 is based on engineering simulation finite element software, such as Abaqus, Ansys, and the like.
- the iterative operation component 203 sets the boundary conditions of the iterative operation, the boundary conditions include: total hold time, total time, maximum allowable stress drop and time step; the iterative operation component executes the iterative operation steps.
- the iterative operation component 203 also performs iterative operations:
- each iteration step the displacement control intermediate variable and the load control intermediate variable are calculated, and the result variable of each iteration step is calculated based on the displacement control intermediate variable and the load control intermediate variable: stress drop;
- the result display component 204 generates a dual vertical axis graph of strain/stress versus time according to the calculation results output by each iteration step, and displays the relationship between the local stress and strain of the structural danger point of the component and time.
- the result display component 204 For the implementation details of the result display component 204, reference may be made to the aforementioned step S8.
- the time-dependent local stress-strain method and tool software for high-temperature structural strength and life analysis proposed by the present invention aim at the problem of stress-strain prediction in the local area of components, and based on the stress-strain distribution characteristics of components, the traditional differential Neuber formula is modified, and an improved method is proposed. Local stress-strain calculation method.
- the method and tool software simultaneously solve the problem of stress-strain prediction in local areas of components under load control or displacement control.
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Abstract
本发明揭示了提出一种高温结构强度和寿命分析的时间相关局部应力应变方法，该方法针对高温条件工况下的载荷部件，载荷部件具有结构不连续区域，该方法包括：工况参数获取步骤、材料参数获取步骤、弹塑性分析步骤、极限分析步骤、弹性分析步骤、边界条件设置步骤、迭代运算步骤和结果整合步骤。本发明还揭示了一种高温结构强度和寿命分析的时间相关局部应力应变工具软件，该工具软件包括：参数获取组件、有限元建模及运算组件、迭代运算组件和结果展示组件。
Description
本发明涉及计算机仿真模拟技术领域，更具体地说，涉及高温结构强度和寿命分析的计算机仿真技术。
随着国家节能降耗以及环保等方面的迫切需要，发展新一代先进超超临界汽轮机机组技术已成为国内火电、核电等行业面临的重要课题。在先进能源装备中，大量工程部件面临着高温、高压等极端操作条件。例如，快堆核电系统中的中间热交换器支撑，其正常工作温度540℃，瞬态工况下温度可达610℃，均超过了对应材料316H不锈钢的蠕变起始温度。因此，蠕变变形与断裂问题是核电高温结构强度设计与安全评价需要重点关注的失效模式。
针对受单轴载荷下均匀构件，在确定初始应力应变后即可根据蠕变本构方程计算出该结构在蠕变行为下的应力应变响应。而实际构件其几何结构往往存在较多的结构不连续区域如开孔、倒角等，该区域存在显著的应力应变集中。该区域危险点蠕变应力应变行为的准确计算是结构完整性评价的重要环节。现有时间无关的局部应力应变方法(如Neuber方法等)不能描述高温结构的时间相关蠕变行为，部分研究人员将Neuber方程推广至高温结构应力应变响应预测时通常导致一定误差，如何构建更为精准的应力应变方法，即时间相关的局部应力应变方法是当前结构完整性领域面临的重要课题。
综上所述，现有弹性分析中对应力集中区域危险点处蠕变应力应变行为的预测方法并未能考虑到结构和载荷类型影响，从而导致分析结果产生过度保守或不保守的情况。因此亟待提出一种改进的时间相关局部应力应变方法，实现应力集中区域危险点的准确预测。
发明内容
根据本发明的一实施例，提出一种高温结构强度和寿命分析的时间相关局部应力应变方法，该方法针对高温条件工况下的载荷部件，所述载荷部件具有结构不连续区域，该方法包括：
工况参数获取步骤，工况参数包括设计温度、设计载荷、总保载时间、 部件的材料和部件的结构危险点，所述部件的结构危险点与结构不连续区域相关；
材料参数获取步骤，材料参数包括材料的蠕变本构方程、弹性模量、泊松比、应力应变关系曲线以及等效弹性模量，根据材料参数和工况参数建立有限元模型；
弹塑性分析步骤，基于有限元模型进行弹塑性分析，确定部件的结构危险点的初始等效应力、初始等效应变和远场区域初始应力；
极限分析步骤，基于有限元模型进行极限分析，确定极限载荷和结构危险点的初始参考应力；
弹性分析步骤，基于有限元模型进行弹性分析，确定结构危险点的弹性应力、弹性应变和应力集中因子；
边界条件设置步骤，设置迭代运算的边界条件，边界条件包括：总保载时间、总时间、最大允许应力降和时间步长；
迭代运算步骤，
每一迭代步中，计算位移控制中间变量和载荷控制中间变量，基于位移控制中间变量和载荷控制中间变量计算每一迭代步的结果变量：应力降；
将应力降与最大允许应力降比较，如果应力降大于最大允许应力降，则调整时间步长后重新计算该迭代步的中间变量和结果变量；
如果应力降不大于最大允许应力降，则输出该迭代步的计算结果：总应力、总应变、参考应力、参考应变、远场应力和总保载时间；
判断计算时间是否达到总时间，如果达到总时间则迭代步骤结束；
如果没有达到总时间则进入下一个迭代步。
结果整合步骤，根据各个迭代步输出的计算结果，确定部件的结构危险点的局部应力应变与时间的关联关系。
在一个实施例中，所述材料参数获得步骤中，
材料参数通过查询材料性能库获得：
在材料性能库中，获取所述材料在设计温度T条件下的弹性模量E和泊松比v、蠕变本构方程
其中
为蠕变应变率，σ为应力，A为蠕变本构参数，n为蠕变本构方程中的应力指数参数，并计算等效弹性模量
在材料性能库中，获取所述材料在设计温度T条件下的应力应变关系曲线；
或者，材料参数通过试验获得：
对所述材料采用静态法测试或者动态热机械分析仪测试，获得设计温度T下的弹性模量E和泊松比v，
对所述材料进行设计温度T下的圆棒拉伸蠕变试验，获得蠕变本构方程
其中
为蠕变应变率，σ为应力，A为蠕变本构参数，n为蠕变本构方程中的应力指数参数，
计算等效弹性模量
对所述材料进行设计温度T下的圆棒拉伸试验，获得材料的塑性延伸强度，并根据塑性延伸强度获得材料的应力应变关系曲线。
在一个实施例中，极限分析步骤中，基于有限元模型进行极限分析获得极限载荷P
L，并根据极限载荷计算结构危险点的初始参考应力
其中P是设计载荷，P
L是极限载荷，σ
y是屈服强度。
在一个实施例中，弹性分析步骤中，通过基于有限元模型进行弹性分析确定结构危险点的弹性应力σ
elastic和弹性应变ε
elastic，然后计算结构危险点的应力集中因子K
t；
其中，E为弹性模量，σ
ref为结构危险点的初始参考应力。
在一个实施例中，迭代运算步骤中，位移控制中间变量包括：蠕变应变增量、远场蠕变增量、参考应力降、远场弹性应变增量和参考应变增量；
当部件受位移控制时，对于每一迭代步i，根据所述蠕变本构方程
分别计算迭代步i对应的蠕变应变增量
远场蠕变应变增量
并计算迭代步i对应的参考应力降
其中A为蠕变本构参数，E为弹性模量，Δt是时间步长；
迭代步i对应的远场弹性应变增量
其中Δt是时间步长，
是初始应力；
以及迭代步i对应的参考应变增量
在一个实施例中，迭代运算步骤中，载荷控制中间变量包括：蠕变应变增量和参考应变增量；
当部件受载荷控制时，对于每一迭代步i，远场蠕变应变增量
远场弹性应变增量
参考应力降
参考蠕变增量
计算如下：
其中A为蠕变本构参数，Δt是时间步长。
在一个实施例中，迭代运算步骤中，对于每一迭代步i，结果变量：应力降Δσ
i计算如下：
其中K是应力集中因子，ε
c为蠕变应变，ε为等效应变，σ为应力。
在一个实施例中，迭代运算步骤中，对于每一迭代步i，如果应力降Δσ
i不大于最大允许应力降σ
allow，则输出该迭代步的计算结果：总应力σ
i、总应变ε
i、参考应力
参考应变
远场应力
以及总保载时间t
i，
总应力σ
i计算如下：
σ
i＝σ
i-1+Δσ
i；
总应变ε
i计算如下：
其中
为等效弹性模量；
参考应力
计算如下：
参考应变
计算如下：
远场应力
计算如下：
总保载时间t
i计算如下：
t
i＝t
i-1+Δt。
在一个实施例中，结构危险点根据应力场从结构不连续区域中选择。
根据本发明的一实施例，提出一种高温结构强度和寿命分析的时间相关局部应力应变工具软件，所述工具软件基于有限元软件，该工具软件针对高温条件工况下的载荷部件，所述载荷部件具有结构不连续区域，所述工具软件包括：参数获取组件、有限元建模及运算组件、迭代运算组件和结果展示组件。
参数获取组件获取工况参数和材料参数，工况参数包括设计温度、设计载荷、总保载时间、部件的材料和部件的结构危险点，所述部件的结构危险点与结构不连续区域相关；材料参数包括材料的蠕变本构方程、弹性模量、泊松比、应力应变关系曲线以及等效弹性模量。
有限元建模及运算组件，根据材料参数建立有限元模型；基于有限元模型进行弹塑性分析，确定部件的结构危险点的初始等效应力、初始等效应变和远场区域初始应力；基于有限元模型进行极限分析，确定极限载荷和结构危险点的初始参考应力；基于有限元模型进行弹性分析，确定结构危险 点的弹性应力、弹性应变和应力集中因子。
迭代运算组件设置迭代运算的边界条件，边界条件包括：总保载时间、总时间、最大允许应力降和时间步长；迭代运算组件执行迭代运算步骤，每一迭代步中，计算位移控制中间变量和载荷控制中间变量，基于位移控制中间变量和载荷控制中间变量计算每一迭代步的结果变量：应力降；将应力降与最大允许应力降比较，如果应力降大于最大允许应力降，则调整时间步长后重新计算该迭代步的中间变量和结果变量；如果应力降不大于最大允许应力降，则输出该迭代步的计算结果：总应力、总应变、参考应力、参考应变、远场应力和总保载时间；判断计算时间是否达到总时间，如果达到总时间则迭代步骤结束；如果没有达到总时间则进入下一个迭代步。
结果展示组件根据各个迭代步输出的计算结果，生成应变/应力-时间的双纵轴图表，展示部件的结构危险点的局部应力应变与时间的关联关系。
本发明提出的高温结构强度和寿命分析的时间相关局部应力应变方法及工具软件针对构件局部区域的应力应变预测问题，基于构件的应力应变分布特征，对传统微分Neuber式进行修正，提出了改进的局部应力应变计算方法。综上，该方法和工具软件同时解决了载荷控制或位移控制下构件局部区域应力应变预测问题。
图1揭示了根据本发明的一实施例的高温结构强度和寿命分析的时间相关局部应力应变方法的流程图。
图2揭示了根据本发明的一实施例的高温结构强度和寿命分析的时间相关局部应力应变方法的一具体示例中载荷部件的形状，该载荷部件是简化螺栓部件。
图3揭示了图2所示的示例的简化螺栓部件的结构危险点处蠕变应力应变行为。
图4揭示了根据本发明的一实施例的高温结构强度和寿命分析的时间相关局部应力应变工具软件的结构框图。
针对现有技术的弹性分析中对应力集中区域危险点处蠕变应力应变行为的预测方法并未能考虑到结构和载荷类型影响的缺陷，本发明提出一种高温结构强度和寿命分析的时间相关局部应力应变方法，该方法针对高温条件工况下的载荷部件，该载荷部件具有结构不连续区域。该方法包括：
S1、工况参数获取步骤。工况参数包括设计温度、设计载荷、总保载时间、部件的材料和部件的结构危险点，其中部件的结构危险点与结构不连续区域相关。在一个实施例中，结构危险点根据应力场从结构不连续区域中选择。
S2、材料参数获取步骤。材料参数包括材料的蠕变本构方程、弹性模量、泊松比、应力应变关系曲线以及等效弹性模量，根据材料参数和工况参数建立有限元模型。材料参数的获得有两种方式：通过查询材料性能库获得或者通过试验。在一个实施例中，材料参数获得步骤中，材料参数通过查询材料性能库获得：
在材料性能库中，获取所述材料在设计温度T条件下的弹性模量E和泊松比v、蠕变本构方程
其中
为蠕变应变率，σ为应力，A为蠕变本构参数，n为蠕变本构方程中的应力指数参数，计算等效弹性模量
在材料性能库中，获取所述材料在设计温度T条件下的应力应变关系曲线。
或者，在另一个实施例中，材料参数可以通过试验获得：
对所述材料采用静态法测试或者动态热机械分析仪测试，获得设计温度T下的弹性模量E和泊松比v，静态法测试或者动态热机械分析仪测试都可以用于获取弹性模量E和泊松比v，
对所述材料进行设计温度T下的圆棒拉伸蠕变试验，获得蠕变本构方程
其中
为蠕变应变率，σ为应力，A为蠕变本构参数，n为蠕变本构方程中的应力指数参数，
计算等效弹性模量
对材料进行设计温度T下的圆棒拉伸试验，获得材料的塑性延伸强度，并根据塑性延伸强度获得材料的应力应变关系曲线。
在步骤S2中会根据材料参数和工况参数建立有限元模型。在一个实施例中，建立有限元模型会使用工程模拟有限元软件。比如主要针对进行结构力学分析的有限元软件，例如Abaqus、Ansys等。
S3、弹塑性分析步骤。基于有限元模型进行弹塑性分析，确定部件的结构危险点的初始等效应力、初始等效应变和远场区域初始应力。
S4、极限分析步骤。基于有限元模型进行极限分析，确定极限载荷和结构危险点的初始参考应力。在一个实施例中，在极限分析步骤中，基于有限元模型进行极限分析获得极限载荷P
L，并根据极限载荷计算结构危险点的初始参考应力
其中P是设计载荷，P
L是极限载荷，σ
t是屈服强度，即0.2％塑性变形对应的应力)
S5、弹性分析步骤。基于有限元模型进行弹性分析，确定结构危险点的弹性应力、弹性应变和应力集中因子。在一个实施例中，弹性分析步骤中，通过基于有限元模型进行弹性分析确定结构危险点的弹性应力σ
elastic和弹性应变ε
elastic，然后计算结构危险点的应力集中因子K
t；
其中，E为弹性模量，σ
ref为结构危险点的初始参考应力。
S6、边界条件设置步骤。设置迭代运算的边界条件，边界条件包括：总保载时间、总时间、最大允许应力降和时间步长。
S7、迭代运算步骤：
每一迭代步中，计算位移控制中间变量和载荷控制中间变量，基于 位移控制中间变量和载荷控制中间变量计算每一迭代步的结果变量：应力降；
将应力降与最大允许应力降比较，如果应力降大于最大允许应力降，则调整时间步长后重新计算该迭代步的中间变量和结果变量；
如果应力降不大于最大允许应力降，则输出该迭代步的计算结果：总应力、总应变、参考应力、参考应变、远场应力和总保载时间；
判断计算时间是否达到总时间，如果达到总时间则迭代步骤结束；
如果没有达到总时间则进入下一个迭代步。
在一个实施例中，在S7迭代运算步骤中，位移控制中间变量包括：蠕变应变增量、远场蠕变增量、参考应力降、远场弹性应变增量和参考应变增量；
当部件受位移控制时，对于每一迭代步i，根据所述蠕变本构方程
分别计算迭代步i对应的蠕变应变增量
远场蠕变应变增量
并计算迭代步i对应的参考应力降
其中A为蠕变本构参数，E为弹性模量，Δt是时间步长；
迭代步i对应的远场弹性应变增量
其中Δt是时间步长，
是初始应力；
以及迭代步i对应的参考应变增量
在一个实施例中，在S7迭代运算步骤中，载荷控制中间变量包括：蠕变应变增量和参考应变增量；
当部件受载荷控制时，对于每一迭代步i，远场蠕变应变增量
远场弹性应变增量
参考应力降
参考蠕变增量
计算如下：
其中A为蠕变本构参数，Δt是时间步长。
在一个实施例中，在S7迭代运算步骤中，对于每一迭代步i，结果变量：应力降Δσ
i计算如下：
其中K是应力集中因子，ε
c为蠕变应变，ε为等效应变，σ为应力。
在一个实施例中，在S7迭代运算步骤中，对于每一迭代步i，如果应力降Δσ
i不大于最大允许应力降σ
allow，则输出该迭代步的计算结果：总应力σ
i、总应变ε
i、参考应力
参考应变
远场应力
以及总保载时间t
i，
总应力σ
i计算如下：
σ
i＝σ
i-1+Δσ
i；
总应变ε
i计算如下：
其中
为等效弹性模量；
参考应力
计算如下：
参考应变
计算如下：
远场应力
计算如下：
总保载时间t
i计算如下：
t
i＝t
i-1+Δt。
S8、结果整合步骤，根据各个迭代步输出的计算结果，确定部件的结构危险点的局部应力应变与时间的关联关系。
图1揭示了根据本发明的一实施例的高温结构强度和寿命分析的时间相关局部应力应变方法的流程图。参考图1所示，该实施例的方法包括如下的步骤：
S
101、获取设计工况参数，工况参数包括：设计温度T、设计载荷P、设计总保载时间t
total、高温结构或部件的具体材料和结构尺寸。
S
102、根据步骤S
1中的材料和设计温度T，获得材料参数，材料参数包括：蠕变本构方程(以Norton本构方程为例，见下式)，弹性模量E，泊松比v，应力应变关系曲线以及等效弹性模量
其中
为蠕变应变率，σ为应力，A为蠕变本构参数，n为蠕变本构方程中的应力指数参数。材料参数可以通过查询材料性能库获得，材料参数也可以通过试验获得。如果是通过试验获得材料参数，弹性模量E和泊松比v，可以通过静态法测试或者动态热机械分析仪测试获得。蠕变本构方程可以通过圆棒拉伸蠕变试验获得。应力应变关系曲线可以通过圆棒拉伸试验获得。
S
103、在有限元软件，比如Abaqus或者Ansys中基于有限元方法对高温结构或部件进行弹-塑性分析，确定结构不连续区域所关注的危险点的初始应力σ
0和初始等效应变ε
0以及远场区域的初始应力
(也可根据名义应力理论式确定)，以上应力均为von-Mises应力。
S
104、通过极限分析确定结构极限载荷P
L，并依据下式求取对应初始参考应力
P是设计载荷，P
L是极限载荷，σ
y是屈服强度，即0.2％塑性变形对应的应力。
S
105、通过弹性分析，确定结构不连续区域所关注的危险点的弹性应力σ
elastic和弹性应变ε
elastic，然后依据下式求取对应的应力集中因子K
t；
其中，E为弹性模量，σ
ref为结构危险点的初始参考应力。
S
106、设定分析所需参量：时间步长Δt，总保载时间t
total，每步最大允许应力降σ
allow。时间步长Δt，总保载时间t
total，每步最大允许应力降σ
allow为迭代运算的边界条件。
S
107、当结构受位移控制时，依照S
2中的蠕变本构方程分别求取迭代步i对应的蠕变应变增量
远场蠕变应变增量
并依据下式分别求取迭代步i对应的参考应力降
迭代步i对应的远场弹性应变增量
以及迭代步i对应的参考应变增量
当结构受载荷控制时,迭代步i对应的远场蠕变应变增量
远场弹性应变增量
参考应力降
而参考蠕变增量
由下式计算。
S
108、依照下式求取对应迭代步i的应力降Δσ
i；
S
109、判定迭代步i的应力降Δσ
i是否满足S
6步设定的最大允许应力降σ
allow。若满足则继续S
110，如不满足则调整时间步长Δt，并对迭代步i重复S
107-S
109。
S
110、更新迭代步i对应保载时间下的总应力σ
i、总应变ε
i、参考应力
参考应变
远场应力
以及总保载时间t
i，并对以上量进行输出。对应计算式如下：
σ
i＝σ
i-1+Δσ
i
t
i＝t
i-1+Δt
S
111、判定迭代步i对应保载时间t
i是否满足大于等于总保载时间t
total；若满足则停止迭代计算，否则进行第i+1步迭代计算。
下面结合图2和图3介绍根据本发明的一实施例的高温结构强度和寿命分析的时间相关局部应力应变方法的一具体实现示例。在该具体实现示例中，载荷部件是螺栓部件。现在需要针对螺栓部件求取蠕变条件下螺牙根部的应力应变响应。螺栓设计温度为538℃，设计位移载荷为0.171mm，设计寿命为30000小时，部件材料为316不锈钢，图2揭示了该螺栓部件的简化建模模型，即在该示例中，载荷部件是简化螺栓部件。
执行的工艺流程如下：
步骤1、获取设计工况参数。螺栓设计温度T为538℃，设计位移载荷为0.171mm，设计寿命t
total为30000小时，部件材料为316不锈钢，结构尺寸参考图2所示：螺栓直径20mm、螺牙直径18mm、螺牙长度0.73mm、螺牙与螺栓的过渡倾斜面的倾斜角度为15度。
步骤2、获取材料性能数据。采用静态法测试获得538℃下的弹性模量E为164GPa，泊松比v为0.3。进行538℃下圆棒拉伸试验，测试获得0.2％塑性延伸强度R
P0.2为136MPa。进行538℃下高温圆棒拉伸蠕变试验，测试获得蠕变本构方程
步骤3、根据螺栓部件的几何参数和材料性能数据，基于弹塑性有限元分析确定螺纹牙底最大应力点处的初始应力σ
0＝115.06MPa，初始等效应变ε
0＝7.01e-4以及远场区域初始应力
步骤4、根据螺栓部件的几何参数和材料性能数据，基于极限分析确定结构极限载荷P
L＝109.375MPa和初始参考应力
步骤5、设定分析所需参量：Δt＝0.1s，t
total＝30000h，σ
allow＝0.1MPa。
步骤6、按照前述S
107-S
111编写迭代计算程序，将以上参数输入迭代计算程序中，开展迭代计算。
步骤7、基于迭代计算结果，得到位移载荷下构件危险点处蠕变应力应变行为，如图3所示。图3揭示了图2所示的示例的简化螺栓部件的结构危险点处蠕变应力应变行为。图3是一个双纵轴坐标图，横坐标是蠕变保载时间，单位是小时。左侧纵坐标是应力，在图示的实施例中是von-Mises应力，单位是Mpa。右侧纵坐标是等效应变。图3中实线曲线表示应力，虚线曲线表 示应变。
本发明还提出一种高温结构强度和寿命分析的时间相关局部应力应变工具软件。图4揭示了根据本发明的一实施例的高温结构强度和寿命分析的时间相关局部应力应变工具软件的结构框图。该工具软件基于有限元软件，该工具软件针对高温条件工况下的载荷部件，载荷部件具有结构不连续区域。参考图4所示，该工具软件包括：参数获取组件201、有限元建模及运算组件202、迭代运算组件203和结果展示组件204。
参数获取组件201获取工况参数和材料参数，工况参数包括设计温度、设计载荷、总保载时间、部件的材料和部件的结构危险点，部件的结构危险点与结构不连续区域相关。材料参数包括材料的蠕变本构方程、弹性模量、泊松比、应力应变关系曲线以及等效弹性模量。参数获取组件201的实现细节可以参考前述的步骤S1和步骤S2。
有限元建模及运算组件202根据材料参数建立有限元模型；基于有限元模型进行弹塑性分析，确定部件的结构危险点的初始等效应力、初始等效应变和远场区域初始应力；基于有限元模型进行极限分析，确定极限载荷和结构危险点的初始参考应力；基于有限元模型进行弹性分析，确定结构危险点的弹性应力、弹性应变和应力集中因子。在一个实施例中，有限元建模及运算组件202基于工程模拟有限元软件，比如Abaqus、Ansys等。有限元建模及运算组件202的实现细节可以参考前述的步骤S3、步骤S4和步骤S5。
迭代运算组件203设置迭代运算的边界条件，边界条件包括：总保载时间、总时间、最大允许应力降和时间步长；迭代运算组件执行迭代运算步骤。迭代运算组件203还进行迭代运算：
每一迭代步中，计算位移控制中间变量和载荷控制中间变量，基于位移控制中间变量和载荷控制中间变量计算每一迭代步的结果变量：应力降；
将应力降与最大允许应力降比较，如果应力降大于最大允许应力降，则调整时间步长后重新计算该迭代步的中间变量和结果变量；
如果应力降不大于最大允许应力降，则输出该迭代步的计算结果：总应力、总应变、参考应力、参考应变、远场应力和总保载时间；
判断计算时间是否达到总时间，如果达到总时间则迭代步骤结束；
如果没有达到总时间则进入下一个迭代步。
迭代运算组件203的实现细节可以参考前述的步骤S6和步骤S7。
结果展示组件204根据各个迭代步输出的计算结果，生成应变/应力-时间的双纵轴图表，展示部件的结构危险点的局部应力应变与时间的关联关系。结果展示组件204的实现细节可以参考前述的步骤S8。
本发明提出的高温结构强度和寿命分析的时间相关局部应力应变方法及工具软件针对构件局部区域的应力应变预测问题，基于构件的应力应变分布特征，对传统微分Neuber式进行修正，提出了改进的局部应力应变计算方法。综上，该方法和工具软件同时解决了载荷控制或位移控制下构件局部区域应力应变预测问题。
Claims (10)
- 一种高温结构强度和寿命分析的时间相关局部应力应变方法，其特征在于，所述方法针对高温条件工况下的载荷部件，所述载荷部件具有结构不连续区域，所述方法包括：工况参数获取步骤，工况参数包括设计温度、设计载荷、总保载时间、部件的材料和部件的结构危险点，所述部件的结构危险点与结构不连续区域相关；材料参数获取步骤，材料参数包括材料的蠕变本构方程、弹性模量、泊松比、应力应变关系曲线以及等效弹性模量，根据材料参数和工况参数建立有限元模型；弹塑性分析步骤，基于有限元模型进行弹塑性分析，确定部件的结构危险点的初始等效应力、初始等效应变和远场区域初始应力；极限分析步骤，基于有限元模型进行极限分析，确定极限载荷和结构危险点的初始参考应力；弹性分析步骤，基于有限元模型进行弹性分析，确定结构危险点的弹性应力、弹性应变和应力集中因子；边界条件设置步骤，设置迭代运算的边界条件，边界条件包括：总保载时间、总时间、最大允许应力降和时间步长；迭代运算步骤，每一迭代步中，计算位移控制中间变量和载荷控制中间变量，基于位移控制中间变量和载荷控制中间变量计算每一迭代步的结果变量：应力降；将应力降与最大允许应力降比较，如果应力降大于最大允许应力降，则调整时间步长后重新计算该迭代步的中间变量和结果变量；如果应力降不大于最大允许应力降，则输出该迭代步的计算结果：总应力、总应变、参考应力、参考应变、远场应力和总保载时间；判断计算时间是否达到总时间，如果达到总时间则迭代步骤结束；如果没有达到总时间则进入下一个迭代步。结果整合步骤，根据各个迭代步输出的计算结果，确定部件的结构危险点的局部应力应变与时间的关联关系。
- 如权利要求1所述的高温结构强度和寿命分析的时间相关局部应力应变方法，其特征在于，所述材料参数获得步骤中，材料参数通过查询材料性能库获得：在材料性能库中，获取所述材料在设计温度T条件下的弹性模量E和泊松比v、蠕变本构方程其中
为蠕变应变率，σ为应力，A为蠕变本构参数，n为蠕变本构方程中的应力指数参数，并计算等效弹性模量
在材料性能库中，获取所述材料在设计温度T条件下的应力应变关系曲线；或者，材料参数通过试验获得：对所述材料采用静态法测试或者动态热机械分析仪测试，获得设计温度T下的弹性模量E和泊松比v，对所述材料进行设计温度T下的圆棒拉伸蠕变试验，获得蠕变本构方程其中
为蠕变应变率，σ为应力，A为蠕变本构参数，n为蠕变本构方程中的应力指数参数，
计算等效弹性模量
对所述材料进行设计温度T下的圆棒拉伸试验，获得材料的塑性延伸强度，并根据塑性延伸强度获得材料的应力应变关系曲线。 - 如权利要求2所述的高温结构强度和寿命分析的时间相关局部应力应变方法，其特征在于，极限分析步骤中，基于有限元模型进行极限分析获得极限载荷P L，并根据极限载荷计算结构危险点的初始参考应力
其中P是设计载荷，P L是极限载荷，σ y是屈服强度。 - 如权利要求3所述的高温结构强度和寿命分析的时间相关局部应力应变方法，其特征在于，弹性分析步骤中，通过基于有限元模型进行弹性分析确定结构危险点的弹性应力σ elastic和弹性应变ε elastic，然后计算结构危险点的应力集中因子K t；
其中，E为弹性模量，σ ref为结构危险点的初始参考应力。 - 如权利要求4所述的高温结构强度和寿命分析的时间相关局部应力应变方法，其特征在于，迭代运算步骤中，位移控制中间变量包括：蠕变应变增量、远场蠕变增量、参考应力降、远场弹性应变增量和参考应变增量；当部件受位移控制时，对于每一迭代步i，根据所述蠕变本构方程分别计算迭代步i对应的蠕变应变增量
远场蠕变应变增量
并计算迭代步i对应的参考应力降
其中A为蠕变本构参数，E为弹性模量，Δt是时间步长；迭代步i对应的远场弹性应变增量
其中Δt是时间步长，是初始应力；
以及迭代步i对应的参考应变增量
- 如权利要求5所述的高温结构强度和寿命分析的时间相关局部应力应 变方法，其特征在于，迭代运算步骤中，载荷控制中间变量包括：蠕变应变增量和参考应变增量；当部件受载荷控制时，对于每一迭代步i，远场蠕变应变增量远场弹性应变增量
参考应力降
参考蠕变增量
计算如下：
其中A为蠕变本构参数，Δt是时间步长。 - 如权利要求6所述的高温结构强度和寿命分析的时间相关局部应力应变方法，其特征在于，迭代运算步骤中，对于每一迭代步i，结果变量：应力降Δσ i计算如下：
其中K是应力集中因子，ε c为蠕变应变，ε为等效应变，σ为应力。 - 如权利要求7所述的高温结构强度和寿命分析的时间相关局部应力应变方法，其特征在于，迭代运算步骤中，对于每一迭代步i，如果应力降Δσ i不大于最大允许应力降σ allow，则输出该迭代步的计算结果：总应力σ i、总应变ε i、参考应力参考应变
远场应力
以及总保载时间t i，
总应力σ i计算如下：σ i＝σ i-1+Δσ i；总应变ε i计算如下：
其中为等效弹性模量；
参考应力计算如下：
参考应变计算如下：
远场应力计算如下：
总保载时间t i计算如下：t i＝t i-1+Δt。 - 如权利要求1所述的高温结构强度和寿命分析的时间相关局部应力应变方法，其特征在于，所述结构危险点根据应力场从结构不连续区域中选择。
- 一种高温结构强度和寿命分析的时间相关局部应力应变工具软件，其特征在于，所述工具软件基于有限元软件，该工具软件针对高温条件工况下的载荷部件，所述载荷部件具有结构不连续区域，所述工具软件包括：参数获取组件，参数获取组件获取工况参数和材料参数，工况参数包括设计温度、设计载荷、总保载时间、部件的材料和部件的结构危险点，所述部件的结构危险点与结构不连续区域相关；材料参数包括材料的蠕变本构方程、弹性模量、泊松比、应力应变关系曲线以及等效弹性模量；有限元建模及运算组件，有限元建模及运算组件，根据材料参数建立有限元模型；基于有限元模型进行弹塑性分析，确定部件的结构危险点的初始等效应力、初始等效应变和远场区域初始应力；基于有限元模型进行极限分析，确定极限载荷和结构危险点的初始参考应力；基于有限元模型进行弹性分析，确定结构危险点的弹性应力、弹性应变和应力集中因子；迭代运算组件，迭代运算组件设置迭代运算的边界条件，边界条件包括：总保载时间、总时间、最大允许应力降和时间步长；迭代运算组件执行迭代运算步骤，每一迭代步中，计算位移控制中间变量和载荷控制中间变量，基于位移控制中间变量和载荷控制中间变量计算每一迭代步的结果变量：应力降；将应力降与最大允许应力降比较，如果应力降大于最大允许应力降， 则调整时间步长后重新计算该迭代步的中间变量和结果变量；如果应力降不大于最大允许应力降，则输出该迭代步的计算结果：总应力、总应变、参考应力、参考应变、远场应力和总保载时间；判断计算时间是否达到总时间，如果达到总时间则迭代步骤结束；如果没有达到总时间则进入下一个迭代步。结果展示组件，根据各个迭代步输出的计算结果，生成应变/应力-时间的双纵轴图表，展示部件的结构危险点的局部应力应变与时间的关联关系。
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| CN114692318A (zh) * | 2022-06-01 | 2022-07-01 | 中国飞机强度研究所 | 飞机冲击动力学测试用格栅式燃油箱结构抗毁伤评估方法 |
| CN115130259A (zh) * | 2022-06-24 | 2022-09-30 | 武汉大学 | 跨断层管道接口轴向位移预测、模型构建方法及装置 |
| CN115130259B (zh) * | 2022-06-24 | 2023-10-03 | 武汉大学 | 跨断层管道接口轴向位移预测、模型构建方法及装置 |
| CN115620843A (zh) * | 2022-10-27 | 2023-01-17 | 中国科学院近代物理研究所 | 用于反应堆棒状燃料非线性力学性能分析的计算方法 |
| CN115620843B (zh) * | 2022-10-27 | 2023-06-09 | 中国科学院近代物理研究所 | 用于反应堆棒状燃料非线性力学性能分析的计算方法 |
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| CN115828710B (zh) * | 2023-01-28 | 2023-09-08 | 湖南经研电力设计有限公司 | 电缆支架金具的不均匀厚度设计方法及系统 |
| CN116205116A (zh) * | 2023-05-05 | 2023-06-02 | 江铃汽车股份有限公司 | 一种评估波纹管强度的cae分析方法及系统 |
| CN116312902A (zh) * | 2023-05-25 | 2023-06-23 | 中国科学院力学研究所 | 一种确定材料Johnson-Cook动态本构模型的方法 |
| CN117558381A (zh) * | 2024-01-12 | 2024-02-13 | 四川大学 | 一种金属材料温度与应变速率相关塑性硬化模型计算方法 |
| CN117558381B (zh) * | 2024-01-12 | 2024-03-22 | 四川大学 | 一种金属材料温度与应变速率相关塑性硬化模型计算方法 |
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