Axisymmetric Peridynamic Thermomechanical Coupling Method for Ablation Analysis of Pressure Vessels

Abstract

The present invention discloses an axisymmetric peridynamic thermomechanical coupling method for pressure vessel ablation analysis, which relates to the field of computational mechanics technology. First, a discrete material point model is established to construct a domain; secondly, the thermomechanical coupling problem is determined, and the thermal flow state of the structure at time t is calculated again, and finally the displacement of the material point is calculated. The method establishes an axisymmetric peridynamic thermomechanical coupling analysis model through the non-local construction of deformation gradients and temperature gradients inside and outside the plane, which effectively improves the ability of the peridynamic model in analyzing and predicting the mechanical response of the structural ablation damage; the forward Euler algorithm and the dynamic relaxation algorithm are used to avoid the inconvenience of the stiffness matrix change caused by the change of the degree of freedom of the implicit method; the ablation damage mode of the structure is effectively characterized by a damage criterion, and a fast neighborhood search algorithm is proposed on the basis of the damage criterion to simulate the moving boundary in the ablation process, forming a dynamic update technology of the ablation front, which overcomes the difficulty of confirming the moving boundary in the ablation process.

Description

Technical Field

[0001] The invention relates to the technical field of computational mechanics, and in particular to an axisymmetric peridynamics thermomechanical coupling method for pressure vessel ablation analysis. Background Art

[0002] As the core component of nuclear power plant facilities, the nuclear reactor pressure vessel (RPV) is an indispensable part of the normal operation of the entire reactor. During the service life of the pressure vessel, it is subjected to thermal shock loads, and the thermal stress may suddenly increase sharply at a certain moment, which will have a significant impact on the strength, stiffness, service life and structural integrity of the component.

[0003] Studies have shown that in the event of a severe accident, the reactor pit water injection system is turned on, and the flow of cooling water and the boiling heat exchange on the outer wall of the pressure vessel can promptly remove the core decay heat, thereby ensuring that the pressure vessel wall is not further burned through, causing the molten material to remain in the reactor. However, when the core molten material is retained in the lower head of the pressure vessel, the high heat flux density boundary will directly act on the inner wall of the pressure vessel. At this time, although the decay heat can be removed through the outer wall of the pressure vessel, the inner wall will inevitably undergo ablation, causing it to become thinner, thereby destroying the structural integrity of the pressure vessel. In addition, materials are often accompanied by large mechanical deformations under high temperature and high pressure, which causes huge thermal stresses inside the RPV. Due to the existence of the above-mentioned thermal-mechanical coupling characteristics, the safety analysis of pressure vessels under severe accidents is still very challenging.

[0004] Ablation and its resulting thermomechanical coupling response are difficult and costly to implement experimentally, especially for high-temperature core melts. On the contrary, numerical simulation methods, as a highly efficient numerical calculation method in recent decades, provide a feasible solution for detailed exploration of the ablation behavior and elastic-plastic response of structures under extreme loads. After selecting reasonable ablation and constitutive models, the ablation evolution behavior of the eye container can be predicted quickly and accurately. Therefore, it is extremely important to develop a thermomechanical coupling numerical algorithm that can simulate ablation phenomena with high precision and accuracy.

[0005] In the field of engineering thermal-mechanical coupling analysis, numerical calculation methods such as the finite element method (FEM) based on the continuous medium mechanics model are the most widely used, and commercial software based on FEM is basically mature. Despite this, FEM cannot obtain accurate moving boundaries when dealing with problems such as ablation where the geometric model changes dynamically over time. Therefore, the traditional finite element method can only use limited means to solve the ablation problem. When the geometric model and load are relatively simple, the life-and-death unit method is usually used. When the geometric model or load condition is more complex, the unit deletion technology is used. These traditional methods are difficult to accurately describe the movement of the geometric boundary during the ablation process, and it is even more difficult to track the loading position of the load at all times, which causes some large errors and false residual boundaries in the ablation results.

[0006] In the past two decades, peridynamics (PD) as a new type of non-local model has performed well in dealing with problems with discontinuities and discontinuities. It solves the difficulty of the method based on the continuous medium mechanics model that is not differentiable at geometric discontinuities by converting the differential form of the physical equation in space into an integral form. In addition, pressure vessels have a high degree of axisymmetry and are often simplified to axisymmetric models in engineering to reduce the scale of calculations and reduce the difficulties brought about by three-dimensional numerical calculations. Summary of the invention

[0007] Based on the problems existing in the prior art, the purpose of the present invention is to provide an axisymmetric peridynamic thermomechanical coupling method for pressure vessel ablation analysis, to provide a simple numerical simulation method for thermomechanical coupling analysis of axisymmetric structures composed of metal materials such as pressure vessels, and to broaden the application scope of peridynamic methods in the field of thermomechanical coupling of solid materials; and to effectively reduce the computational scale of three-dimensional peridynamic models when analyzing large structures with axisymmetric characteristics.

[0008] The present invention is achieved through the following technical solutions:

[0009] In a first aspect, the present application provides an axisymmetric peridynamic thermomechanical coupling method for pressure vessel ablation analysis, comprising the following steps:

[0010] Step 1: Establish a discrete material point model, construct a domain, define the interaction radius, and define the material physical and mechanical properties parameters;

[0011] Step 2: Determine the thermal-mechanical coupling problem and calculate the total time t TC , time step Δt for transient heat conduction problems T , the time interval Δt for solving mechanical problems d , Dynamic relaxation method step number n max , apply loads and initialize variables, where the heat conduction problem is currently solved at time t to satisfy t = NT Δt T , where N T =1,2,3,… are time steps;

[0012] Step 3: Calculate the thermal flow state of the structure at time t based on the temperature field, and then use the forward Euler method to perform explicit time-history integration to update the temperature. When the time meets the mechanical problem solving interval N T Δt T ≥N d Δt d When , go to step 4;

[0013] Step 4: According to the temperature field calculation results, the constitutive relationship of RPV metal materials is introduced to calculate the internal force of the structure, and the dynamic relaxation method is used to calculate the displacement of material points. After meeting the convergence criteria, the displacement solution, velocity solution and stress solution within this time interval are obtained, and then return to step 3 to perform the next time interval calculation.

[0014] Furthermore, in step 1, in order to fit the smooth surface of the complex structure of the RPV more accurately, quadrilateral meshing is performed with the help of FEM commercial software. The centroid of the unit is used as the coordinate of the material point, and the volume of the unit is used as the volume of the material point. The system to be solved is discretized into N material points in space. There are k material points in the neighborhood of any material point x. The material point in the neighborhood is x′, and the relative position vector between two material points is ξ.

[0015] Furthermore, in step 3, when considering the ablation behavior under high temperature, the material point deletion technology is used to update the remaining geometric model and the load boundary.

[0016] Furthermore, the geometric model is updated by using a scalar function to determine the ablation damage state of the material point.

[0017]

[0018] When the material point temperature T exceeds its melting point T m After that, the material point is considered to be ablated. At this time, the state of the bond with x and its neighborhood x′ in the peridynamics is μ T <ξ> can be given by the following formula,

[0019]

[0020] The corresponding influence function of the interaction relationship between two material points ω <ξ>Updated to:

[0021] ω (ξ>= μ T <ξ> ω <ξ>;

[0022] Subsequently, a thermal load is applied on the new load boundary to simulate the dynamic ablation effect.

[0023] Furthermore, in step 3, in order to suppress the inherent zero-energy modes in the unconventional state-based peridynamics, a bond-based temperature gradient correction method is introduced to define the correction of the temperature scalar state in Q =T(x′, t)-T(x, t) is the temperature scalar state, For nonlocal temperature gradients, the inhomogeneous part of the temperature scalar state is added to the heat flow scalar state,

[0024]

[0025] Where k is the material thermal conductivity matrix, K is the shape tensor, and q is the heat flux density.

[0026] Furthermore, in step 3, the temperature solution is completed using the forward Euler method, and the specific integration process is given in pseudo code form, including:

[0027] S1: Initialize variables, let N T =0;

[0028] S2: Let N T =N T +1, start loop;

[0029] S2-1: Loop through all material points and use the Nth T Step temperature Computing nonlocal temperature gradients Heat flux q;

[0030] S2-2: Loop through all material points and calculate the heat flow scalar state And the temperature-time derivative

[0031] S2-3: Loop through all material points and calculate

[0032] S3: When N T Δt T ≥N d Δt d , the loop ends.

[0033] Furthermore, in step 4, the Nth d The momentum conservation equation of the step is solved by the dynamic relaxation method. At this time, the time increment Δt in the dynamic relaxation method is transformed into the equation to be solved:

[0034]

[0035] where Λ is the imaginary density diagonal matrix, is the adaptive damping, X and U are the position and displacement vectors of all points respectively, and f is the internal force vector composed of all points;

[0036] The central difference method is used to solve the equation to be solved, and the maximum value of the iteration step n is set when solving the equation. max , the displacement and velocity of the next iteration step are given by the following formula:

[0037]

[0038]

[0039] Where n is the nth step in the iterative process of the dynamic relaxation method. When the first iteration starts, is the adaptive damping coefficient during each iteration and is given by,

[0040]

[0041]

[0042] Among them, the value of the imaginary density diagonal matrix is ​​Λ ii =1, is the virtual stiffness, and the corresponding critical step length of the dynamic relaxation method is E is the elastic modulus of the material.

[0043] Furthermore, in step 4, a key-based deformation gradient correction method for the axisymmetric plane is introduced to define the correction of the deformation vector state in Y is the deformation vector state between two material points, is the in-plane part of the non-local deformation gradient, adding the non-uniform part of the deformation vector state to the force vector state,

[0044] Among them C in The material elastic tensor C is the material elastic tensor C with the remaining part in the out-of-plane direction removed. is the correction factor after considering the axisymmetry, Influence function related variables.

[0045] Furthermore, in step 4, the specific dynamic relaxation method integration process is given in pseudo code form, including:

[0046] S1: Initialize the iteration variable, set n = 0;

[0047] S2: Set n=n+1 and start the loop;

[0048] S2-1: Loop through all material points and use the temperature u according to the peridynamic method n Computing nonlocal deformation gradients and The stress σ is calculated by elastic-plastic constitutive integration;

[0049] S2-2: Loop through all material points and calculate the force vector state and internal force f;

[0050] S2-3: Calculate adaptive damping and

[0051] S2-4: Update displacement U n+1 ;

[0052] S3: When , the loop ends.

[0053] Furthermore, in step 4, the small deformation assumption is considered, the PK1 stress is replaced by the Cauchy stress, and the sequential coupling form of displacement and temperature is considered to achieve the solution of the thermal-mechanical coupling response of the RPV structure under ablation.

[0054] P≈σ=C:(ε-ε T );

[0055] where the total strain ε is calculated from the deformation gradient,

[0056]

[0057] in is the nonlocal deformation gradient; thermal strain ε T Calculated from temperature and thermal expansion coefficient,

[0058] ε T =αTI,

[0059] Where α is the thermal expansion coefficient and I is the unit matrix.

[0060] In a second aspect, the present application provides a computer program, which can implement the steps of the method described above.

[0061] In a third aspect, the present application provides a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the above method.

[0062] In a fourth aspect, the present application provides a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the above method.

[0063] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0064] (1) The axisymmetric peridynamic thermomechanical coupling method for pressure vessel ablation analysis provided by the present invention provides a simple numerical simulation method for thermomechanical coupling analysis of axisymmetric structures composed of metal materials such as pressure vessels, and broadens the application scope of peridynamic methods in the field of thermomechanical coupling of solid materials. It effectively reduces the computational scale of three-dimensional peridynamic models when analyzing large structures with axisymmetric characteristics. In addition, the use of a meshless method to solve the equations in the axisymmetric peridynamic thermomechanical coupling model reduces the complexity of the numerical implementation process and avoids problems such as stiffness singularity;

[0065] (2) The axisymmetric peridynamic thermomechanical coupling method for pressure vessel ablation analysis provided by the present invention provides an effective particle deletion technology for simulating the boundary movement phenomenon during the ablation process of metal structures. The metal melting temperature is used as a judgment condition, combined with the classification of material point states, to overcome the shortcomings of the traditional finite element method in that it is difficult to apply loads on the moving boundary or it is difficult to determine the moving boundary.

[0066] (3) The axisymmetric near-field dynamic thermomechanical coupling method for pressure vessel ablation analysis provided by the present invention provides a high-precision numerical simulation method for the thermomechanical coupling analysis of metal materials under high-temperature loads. The temperature field and the displacement field are coupled in a sequential coupling manner, and an explicit integral format is used to develop a thermomechanical coupling alternating solution algorithm. This allows the present invention to effectively simulate the metal deformation behavior of the structure under high temperature and accurately analyze the effect of ablation on the metal structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] In order to more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and should not be regarded as limiting the scope. For those of ordinary skill in the art, other relevant drawings can be obtained based on these drawings without creative work. In the drawings:

[0068] Figure 1 The initial configuration and current configuration of the axisymmetric unconventional state-based approach dynamics of the present invention;

[0069] Figure 2 The operation flow chart of the axisymmetric peridynamic thermomechanical coupling method (CA-PD-RPV-A) for pressure vessel ablation analysis of the present invention;

[0070] Figure 3 A schematic diagram of a geometric model and heat flow load of an embodiment of the present invention;

[0071] Figure 4 The temperature distribution cloud diagram at 7200s obtained by using CA-PD-RPV-A and ANSYS software respectively for the embodiments of the present invention;

[0072] Figure 5 It is a local comparison diagram of the remaining configurations of the MPDT of the present invention and the unit deletion technology in FEM;

[0073] Figure 6 The vonMises stress distribution cloud diagram at 7200s obtained by using CA-PD-RPV-A and ANSYS software respectively for the embodiments of the present invention;

[0074] Figure 7 The displacement distribution cloud diagram at 7200s obtained by using CA-PD-RPV-A and ANSYS software respectively for the embodiments of the present invention. DETAILED DESCRIPTION

[0075] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments.

[0076] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0077] The terms "comprises," "comprising," or any other variation thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or apparatus that includes a list of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus that includes the element.

[0078] Example 1

[0079] This embodiment provides an axisymmetric peridynamic thermomechanical coupling method for pressure vessel ablation analysis (CA-PD-RPV-A). In order to accurately capture the mechanical behavior of the axisymmetric structure under thermal shock load and improve the accuracy of the analysis, the present invention analyzes the ablation behavior of the structure under thermal shock load based on an unconventional state-based peridynamic model and studies the change of thermal stress. A method for axisymmetric peridynamic thermomechanical coupling method for pressure vessel ablation analysis is provided. The specific contents are as follows:

[0080] Based on the unconventional state-based peridynamics framework and combined with the characteristics of axisymmetric problems, Figure 1 The corresponding reference configuration and current configuration of the non-ordinary state-based peridynamics model (NOSB-PD) in the axisymmetric plane are given, where x is the position vector of the material point in the reference configuration, y is the position vector of the material point in the current configuration, u is the displacement vector of the material point, T is the force vector state, Y is the deformation vector state, is the circular neighborhood of the material point x with radius δ, ξ = x′-x is the relative position vector in the reference configuration, and η = u′-u is the relative displacement between the material points x and x′. It is worth noting that in the unconventional state-based peridynamics, the force vector state T With deformation vector state Y =y′-y=η+ξ is not necessarily in a parallel state.

[0081] The temperature gradient at the midpoint of an axisymmetric heat conduction problem is expressed as Defining a temperature scalar state related to the temperature T at two points in an axisymmetric peridynamic model Q =T(x′, t)-T(x, t), and its non-local form is:

[0082]

[0083] where K is a tensor of shape, represents the multiplication of two vectors,

[0084]

[0085] Here the degree of interaction between material points is determined by the scalar state ω Description, and the thermal energy density Z of the material point is expressed as a function of the temperature scalar state, that is, Combining the Euler-Lagrange equation, the transient heat conduction equation can be derived:

[0086]

[0087] in H <ξ> and H ′<-ξ> is the heat flux scalar state related to the heat flux density in the peridynamic framework and is written as:

[0088] H <ξ>=- ω <ξ>q·K -1 ·ξ

[0089] H ′<-ξ>=- ω <-ξ>q′·K -1′ ·-ξ (4);

[0090] Different from the scalar field problem, the deformation gradient of the structure in the axisymmetric mode is divided into two parts: in-plane and out-of-plane.

[0091]

[0092] Among them, the non-local form of the in-plane deformation gradient is

[0093]

[0094] The nonlocal form of the out-of-plane deformation gradient is written as: in Non-local displacement vector writing:

[0095]

[0096] The strain energy density at a point is further expressed as Combining the Euler-Lagrange equation, we get the integral-differential form of the momentum conservation equation:

[0097]

[0098] in T <ξ> and T ′<-ξ> is the peridynamic force vector state, written as:

[0099]

[0100] T ′<-ξ>= ω <-ξ>P in′ ·K -1′ ·(-ξ) (9);

[0101] Where (★)′ represents the corresponding variable of point x′, b is the body force, and P is the PK1 stress:

[0102]

[0103] is the correction coefficient after considering the axisymmetry, β′<ξ′>=0;

[0104] The transient heat conduction equation and momentum conservation equation represented by equation (3) and equation (8) are the basic formats of the CA-PD-RPV-A proposed in the present invention, and are solved using numerical methods such as the meshless method.

[0105] The specific implementation steps of CA-PD-RPV-A cycle calculation are as follows:

[0106] Step 1: discretize the RPV structure with an appropriate material point size, assign corresponding material properties to the material points, including physical properties and mechanical properties, determine the set of points in each material point and its neighborhood according to the position coordinates of the discretized material points and the specified peridynamic neighborhood radius δ, and establish the interaction relationship between the material points;

[0107] Step 2: Define the total calculation time t for the thermal-mechanical coupling problem TC , time step Δt of transient heat conduction problem T , total time step of heat conduction NT, time interval for solving mechanical problems Δt d , thermal coupling load step N d , Dynamic relaxation method step number n max , where the current solution time t of the heat conduction problem satisfies t=N T Δt T , N T =1, 2, 3…;

[0108] Step 3: Calculate the thermal flow state of the structure at time t based on the temperature field, and then use the forward Euler method to perform explicit time-history integration to update the temperature. When the time meets the mechanical problem solving interval N T Δt T ≥N d Δt d When , go to step 4;

[0109] Step 4: According to the temperature field calculation results, the classic RPV metal material constitutive relationship is introduced to calculate the internal force of the structure, and the dynamic relaxation method is used to calculate the material point displacement. After meeting the convergence criterion, the displacement solution, velocity solution and stress solution within this time interval are obtained, and then return to step 3 to perform the next time interval calculation.

[0110] In step 1, in order to fit the smooth surface of the complex structure of the RPV more accurately, quadrilateral meshing is performed with the help of FEM commercial software. The centroid of the unit is used as the coordinate of the material point, and the volume of the unit is used as the volume of the material point. The system to be solved is discretized into N material points in space, and there are k material points in the neighborhood of any material point x.

[0111] In step 3, when considering the ablation behavior under high temperature, the material point deletion technique (MPDT) is used to update the remaining geometric model and load boundary. The update of the geometric model uses a scalar function to determine the ablation damage state of the material point.

[0112]

[0113] When the material point temperature T exceeds its melting point T m After that, the material point is considered to be ablated. At this time, the state of the bond with x and its neighborhood x′ in the peridynamics is μ T <ξ> can be given by:

[0114]

[0115] The corresponding influence function ω <ξ>Updated to:

[0116] ω <ξ>= μ T <ξ> ω <ξ> (13);

[0117] Subsequently, a thermal load is applied on the new load boundary to simulate the dynamic ablation effect.

[0118] In step 3, in order to suppress the inherent zero-energy mode in the unconventional state-based peridynamics, the present invention proposes a bond-based temperature gradient correction method to define the correction of the temperature scalar state Adding the inhomogeneous part of the temperature scalar state to the heat flow scalar state yields

[0119]

[0120] Where k is the material thermal conductivity matrix, K is the shape tensor, and q is the heat flux density.

[0121] In step 3, the temperature solution is completed using the forward Euler method. The specific integration process is given in pseudo code form, as follows:

[0122] S1: Initialize variables, let N T =0;

[0123] S2: Let N T =N T +1, start loop;

[0124] S2-1: Loop through all material points and use the Nth T Step temperature Computing nonlocal temperature gradients Heat flux q;

[0125] S2-2: Circulate all material points and calculate the heat flow scalar state according to equation (14) and equation (3) And the temperature-time derivative

[0126] S2-3: Loop through all material points and calculate

[0127] S3: When N T Δt T ≥N d Δt d , the loop ends.

[0128] In step 4, the Nth d The momentum conservation equation of the step is solved by the dynamic relaxation method, where t is no longer a real physical quantity. At this time, the equation to be solved is transformed into:

[0129]

[0130] Where A is the imaginary density diagonal matrix, is the adaptive damping, X and U are the position and displacement vectors of all points respectively, and f is the internal force vector composed of all points on the right side of the equal sign of equation (10). The central difference method is used to solve equation (15). When solving, the maximum iteration step n is set max , the displacement and velocity of the next iteration step are given by the following formula:

[0131]

[0132]

[0133] Where n is the nth step in the iterative process of the dynamic relaxation method. When the first iteration starts, is the adaptive damping coefficient during each iteration and is given by,

[0134]

[0135] Among them, the value of the imaginary density diagonal matrix is ​​Λ ii =1, is the virtual stiffness, and the corresponding critical step length of the dynamic relaxation method is E is the elastic modulus of the material.

[0136] In step 4, the inherent zero-energy mode in peridynamics only exists when solving the deformation gradient in the plane. Therefore, the present invention proposes a bond-based deformation gradient correction method for the axisymmetric plane, defining the correction of the deformation vector state Add the non-uniform part of the deformation vector state to the force vector state,

[0137]

[0138] Among them C in Remove the remaining part in the out-of-plane direction from the material elastic tensor C.

[0139] In step 4, the specific dynamic relaxation method integration process is given in pseudo code form, specifically:

[0140] S1: Initialize the iteration variable, set n = 0;

[0141] S2: Set n=n+1 and start the loop;

[0142] S2-1: Loop through all material points and calculate the nonlocal deformation gradient using the temperature un according to the peridynamic method and The stress σ is calculated by elastic-plastic constitutive integration;

[0143] S2-2: Loop through all material points and calculate the force vector state according to equations (18) and (10) and internal force f;

[0144] S2-3: Calculate adaptive damping according to equations (17) and (16) and

[0145] S2-4: Update the displacement U according to equation (16) n+1 ;

[0146] S2-5: When End the loop.

[0147] In step 4, the present invention considers the small deformation assumption, replaces the PK1 stress with the Cauchy stress, considers the sequential coupling form of displacement and temperature, and realizes the solution of the thermal-mechanical coupling response of the RPV structure under ablation.

[0148] P≈σ=C:(ε-ε T ) (19);

[0149] where ε is calculated by the deformation gradient,

[0150]

[0151] Thermal strain ε TCalculated from temperature and thermal expansion coefficient,

[0152] ε T =αTI (21);

[0153] In summary, combined with Figure 2 The specific implementation process of CA-PD-RPV-A proposed in the present invention will be shown in the following pseudo code form:

[0154] (1) Establish a discrete material point model, construct a neighborhood, define the interaction radius, and define the material physical properties (density ρ, thermal conductivity k T , thermal expansion coefficient α, specific heat capacity c) parameters, mechanical properties (elastic modulus E, Poisson's ratio ν) parameters;

[0155] (2) Determine the total calculation time t of the thermal-mechanical coupling problem TC , time step Δt for transient heat conduction problems T , the time interval Δt for solving mechanical problems d , Dynamic relaxation method step number n max , apply loads and initialize variables such as temperature, velocity and displacement;

[0156] (3) Enter the mechanical problem solution, loop variable N d =0;

[0157] (3.1) Let N d =N d +1;

[0158] (3.2) Enter the heat conduction problem solution, loop variable N T =0;

[0159] (3.2.1) Let N T =N T +1, use the forward Euler method to solve equation (3) to obtain the temperature field response T;

[0160] (3.2.2) Determine the ablation state of the material point according to equation (11) and use MPDT to update the geometric model;

[0161] (3.2.3) If N T Δt T ≥N d Δt d , go to step (3.3), otherwise return to step (3.2.1) and continue the cycle;

[0162] (3.3) loop variable n = 0;

[0163] (3.3.1) Let n = n + 1, and use the dynamic relaxation method to solve equation (10) according to the temperature field information to obtain the displacement field response u;

[0164] (3.3.2) Determine the damage state of the material point according to CPC-FM and update the crack extension;

[0165] (3.3.3) If Go to step (4), otherwise return to step (3.3.1) and continue the cycle;

[0166] (4) Output the calculation file for post-processing.

[0167] Take the ablation process and thermal-mechanical coupling analysis simulation of the RPV lower head (16MnD5 steel material) under IVR conditions as an example (e.g. Figure 3 As shown), the accuracy and effectiveness of the CA-PD-RPV-A proposed in the present invention are further described in detail in combination with the technical scheme and the accompanying drawings.

[0168] Step 1: Establish the RPV structure entity model under IVR condition according to the geometric model information in FEM commercial software, discretize the RPV structure with appropriate material point size, assign corresponding material properties to the material points, including physical properties and mechanical properties, determine the set of points in each material point and its neighborhood according to the position coordinates of the discretized material points and the specified peridynamic neighborhood radius δ, and establish the interaction relationship between the material points;

[0169] Step 2: Define the total calculation time t for the thermal-mechanical coupling problem TC = 259200s, time step Δt for transient heat conduction problem T = 0.1s, total heat conduction time step N T =2592000, time interval for solving mechanical problems Δt d = 3600s, thermal coupling load step N d =72, number of steps of dynamic relaxation method n max =20000;

[0170] Step 3: Calculate the thermal flow state of the structure at time t based on the temperature field, where t = N T Δt T ,N T = 1, 2, 3…, then the forward Euler method is used to perform explicit time-history integration to update the temperature. At each step of the forward Euler method calculation, the MPDT technology is used to determine the ablation and update the model ablation boundary. When the time meets the mechanical problem solving interval N T Δt T ≥N d Δt d When , go to step 4;

[0171] Step 4: According to the temperature field calculation results, the classic RPV metal material constitutive relationship is introduced to calculate the internal force of the structure, and the dynamic relaxation method is used to calculate the material point displacement. After meeting the convergence criterion, the displacement solution, velocity solution and stress solution within this time interval are obtained, and then return to step 3 to perform the next time interval calculation.

[0172] Experimental example: Ablation-elastic analysis of a spherical pressure vessel under extreme thermal loads.

[0173] In step 1, the basic geometric information and load information of the RPV are as follows: Figure 3 As shown, commercial software was used for meshing, the mesh size was 5 mm, and there were 24320 material points in total. A vertical displacement constraint boundary was applied to the upper end face of the RPV, and an equivalent internal pressure boundary of 2.3 MPa was applied to the outer wall of the RPV. The initial temperature value in the entire domain of the RPV was given to be equal to the outer wall temperature value of 127 °C. In addition, the physical and mechanical properties of the materials are shown in Tables 1 and 2.

[0174] Table 1 Physical properties of 16MnD5 steel

[0175]

[0176] Table 2 Elastic modulus, Poisson's ratio, yield strength and tensile strength of 16MnD5 steel

[0177]

[0178]

[0179] After obtaining the computational geometry model and constitutive parameters, the ablation behavior and elastic response of the RPV are analyzed by looping steps 2 to 4. Finally, the contour, temperature distribution, and deformation of the RPV at the most severe ablation moment under given heat input conditions are obtained, and a comparison is made with the commercial software ANSYS, such as Figure 4-Figure 7 As shown. The calculation results show that the peridynamic method provided by the present invention can effectively simulate the ablation process, heat conduction and thermomechanical coupling behavior of RPV under IVR conditions, and accurately obtain the geometric profile, temperature distribution, structural deformation, failure form and other results of the RPV ablation process under IVR conditions. Furthermore, the calculation results show the difference between the birth and death unit method in the commercial software ANSYS and the material point deletion technology proposed in the present invention. The technology proposed in the present invention can more accurately characterize the dynamic ablation situation in the high heat flux density area.

[0180] Example 2

[0181] This embodiment provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the axisymmetric near-field dynamics thermomechanical coupling method for pressure vessel ablation analysis in the above-mentioned embodiment 1.

[0182] The computer device may be a desktop computer, a notebook, a PDA, a cloud server, etc. The computer device may interact with the user through a keyboard, a mouse, a remote control, a touch pad, or a voice control device.

[0183] The storage device includes at least one type of readable storage medium, and the readable storage medium includes flash memory, hard disk, multimedia card, card-type memory (for example, SD or D interface display memory, etc.), random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic memory, disk, optical disk, etc. In some embodiments, the memory may be an internal storage unit of the computer device, for example, a hard disk or memory of the computer device. In other embodiments, the memory may also be an external storage device of the computer device, such as a plug-in hard disk, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (FlashCard), etc. equipped on the computer device. Of course, the memory may also include both an internal storage unit of the computer device and an external storage device. In this embodiment, the memory is often used to store an operating system and various application software installed on the computer device, such as the program code of the axisymmetric near-field dynamics thermal coupling method for running the pressure vessel ablation analysis, etc. In addition, the memory may also be used to temporarily store various types of data that have been output or are to be output.

[0184] The processor may be a central processing unit (CPU), a controller, a microcontroller, a microprocessor, or other data processing chip in some embodiments. The processor is generally used to control the overall operation of the computer device. In this embodiment, the processor is used to run the program code stored in the memory or process data, such as running the program code of the axisymmetric peridynamics thermomechanical coupling method for the pressure vessel ablation analysis.

[0185] Example 3

[0186] This embodiment provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the processor executes the steps of the axisymmetric peridynamic thermomechanical coupling method for pressure vessel ablation analysis.

[0187] The computer-readable storage medium stores an interface display program, and the interface display program can be executed by at least one processor to enable the at least one processor to perform the steps of the axisymmetric near-field dynamics thermomechanical coupling method for pressure vessel ablation analysis.

[0188] Through the description of the above implementation methods, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be implemented by means of software plus a necessary general hardware platform. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, can be embodied in the form of a software product, which is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk), and includes a number of instructions for a terminal device (which can be a mobile phone, computer, server or network device, etc.) to execute the methods described in each embodiment of the present application.

[0189] The specific embodiments described above further describe the purpose, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only the specific embodiments of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention. For those skilled in the art, it is obvious that the present application is not limited to the details of the above exemplary embodiments, and the present application can be implemented in other specific forms without departing from the spirit or basic features of the present application. Therefore, no matter from which point of view, the embodiments should be regarded as exemplary and non-restrictive. The scope of the present application is limited by the attached claims rather than the above description, and it is intended to include all changes within the meaning and scope of the equivalent elements of the claims in the present application.

Claims

1. Axisymmetric peridynamic thermomechanical coupling method for pressure vessel ablation analysis, characterized by: The following steps are involved: Step 1: Establish a discrete material point model, construct a neighborhood, define the interaction radius, and define the material physical and mechanical properties parameters; Step 2: Determine the thermal-mechanical coupling problem and calculate the total time t TC , time step Δt for transient heat conduction problems T , the time interval Δt for solving mechanical problems d , Dynamic relaxation method step number n max , apply loads and initialize variables, where the heat conduction problem is currently solved at time t to satisfy t = N T Δt T , where N T =1,2,3,… are time steps; Step 3: Calculate the thermal flow state of the structure at time t based on the temperature field, and then use the forward Euler method to perform explicit time-history integration to update the temperature. When the time meets the interval N for solving the mechanical problem T Δt T ≥N d Δt d When N d is the load step for the mechanics problem; Step 4: According to the temperature field calculation results, the constitutive relationship of RPV metal materials is introduced to calculate the internal force of the structure, and the dynamic relaxation method is used to calculate the displacement of the material point. After the convergence criterion is met, the displacement solution, velocity solution and stress solution in this time interval are obtained, and then return to step 3 to calculate the next time interval; In step 3, when considering the ablation behavior under high temperature, the material point deletion technology is used to update the remaining geometric model and load boundary; The geometric model is updated through a scalar function To determine the ablation damage state of the material point, When the material point temperature T exceeds its melting point T m After that, the material point is considered to be ablated. At this time, the state of the bond with x and its neighborhood x′ in the peridynamics is μ T <ξ> can be given by the following formula, The corresponding influence function of the interaction relationship between two material points ω <ξ>Updated to: ω <ξ>= μ T <ξ> ω <ξ>; Subsequently, a thermal load is applied on the new load boundary to simulate the dynamic ablation effect, where ξ is the relative position vector between the two material points.

2. The axisymmetric peridynamic thermomechanical coupling method for pressure vessel ablation analysis according to claim 1, characterized in that: In step 3, in order to suppress the inherent zero-energy modes in the unconventional state-based peridynamics, a bond-based temperature gradient correction method is introduced to define the correction term of the temperature scalar state in Q =T(x′, t)-T(x, t) is the temperature scalar state, For nonlocal temperature gradients, the inhomogeneous part of the temperature scalar state is added to the heat flow scalar state, Where k is the material thermal conductivity matrix, K is the shape tensor, and q is the heat flux density.

3. The axisymmetric peridynamic thermomechanical coupling method for pressure vessel ablation analysis according to claim 1, characterized in that: In step 3, the temperature solution is completed using the forward Euler method. The specific integration process is given in pseudo code form, including: S1: Initialize variables, let N T =0; S2: Let N T =N T +1, start loop; S2-1: Loop through all material points and use the Nth T Step temperature Computing nonlocal temperature gradients Heat flux q; S2-2: Loop through all material points and calculate the heat flow scalar state And the temperature-time derivative S2-3: Loop through all material points and calculate S3: When N T Δt T ≥N d Δt d , the loop ends.

4. The axisymmetric peridynamic thermomechanical coupling method for pressure vessel ablation analysis according to claim 1, characterized in that: In step 4, the Nth d The momentum conservation equation of the step is solved by the dynamic relaxation method. At this time, the time increment Δt in the dynamic relaxation method is no longer used as a real physical quantity, and the equation to be solved is transformed into, where Λ is the imaginary density diagonal matrix, is the adaptive damping, X and U are the position and displacement vectors of all points respectively, and f is the internal force vector composed of all points; The central difference method is used to solve the equation to be solved, and the maximum value of the iteration step n is set when solving the equation. max , the displacement and velocity of the next iteration step are given by the following formula: Where n is the nth step in the iterative process of the dynamic relaxation method. When the first iteration starts, is the adaptive damping coefficient during each iteration and is given by, Among them, the value of the imaginary density diagonal matrix is ​​Λ ii =1, corresponding to the critical time step of the dynamic relaxation method E is the elastic modulus of the material.

5. The axisymmetric peridynamic thermomechanical coupling method for pressure vessel ablation analysis according to claim 1, characterized in that: In step 4, a key-based deformation gradient correction method for the axisymmetric plane is introduced to define the correction amount of the deformation vector state Where Y is the deformation vector state between two material points, is the in-plane part of the non-local deformation gradient. The non-uniform part of the deformation vector state is added to the force vector state, and we get where K is the shape tensor in claim 2, C in P is the material elastic tensor C minus the remaining part in the out-of-plane direction. out is the out-of-plane stress part of PK1, is the correction factor after considering the axisymmetry, Influence function related variables.

6. The axisymmetric peridynamic thermomechanical coupling method for pressure vessel ablation analysis according to claim 1, characterized in that: In step 4, the specific dynamic relaxation method integration process is given in pseudo code form, including: S1: Initialize the iteration variable, set n = 0; S2: Set n=n+1 and start the loop; S2-1: Loop through all material points and use the temperature u according to the peridynamic method n Computing nonlocal deformation gradients and The Cauchy stress σ is calculated by elastic-plastic constitutive integration; S2-2: Loop through all material points and calculate the force vector state and internal force f; S2-3: Calculate adaptive damping and S2-4: Update displacement U n+1 ; S3: When , the loop ends.

7. The axisymmetric peridynamic thermomechanical coupling method for pressure vessel ablation analysis according to claim 1, characterized in that: In step 4, considering the small deformation assumption, the PK1 stress P is replaced by the Cauchy stress σ, and the sequential coupling form of displacement and temperature is considered to achieve the solution of the thermal-mechanical coupling response of the RPV structure under ablation. P≈σ=C:(e-e T ), where the total strain ε is calculated from the deformation gradient, in is the nonlocal deformation gradient; thermal strain ε T Calculated from temperature and thermal expansion coefficient, e T =αTI, Where α is the thermal expansion coefficient, I is the unit matrix, C is the material elastic matrix, and T is the material point temperature.

8. A computer-readable storage medium, characterized in that: A computer program is stored, and when the computer program is executed by a processor, the processor executes the steps of the method according to any one of claims 1 to 7.

9. A computer device, characterized in that: The method comprises a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the method according to any one of claims 1 to 7.

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