Isogeometric transient temperature field analysis method fusing life-death unit technology

Abstract

The invention discloses an isogeometric transient temperature field analysis method fusing a life-death unit technology, and relates to the field of computational mechanics, the method comprises the following steps: establishing an NURBS model of isogeometric analysis, and calculating a unit heat transfer matrix, a unit hot melting matrix and a unit load array; judging whether the current calculation unit is in a calculation time domain or not; if not, setting the unit heat transfer matrix and the unit load array as 0; if yes, recovering the load corresponding to the unit heat transfer matrix and the unit load array, and removing the load at the shared boundary of the unit and other units in the calculation time domain; assembling the unit heat transfer matrix, the unit hot melting matrix and the unit load array into an integral matrix, and constructing a heat transfer equation according to the integral matrix; calculating the temperature of the control point according to the heat transfer equation, and determining the temperature field of the final solution domain. Implementation of the isogeometric transient temperature field analysis method under the complex temperature load condition containing the time sequence problem is considered, and application of isogeometric analysis in engineering is promoted.

Description

Technical Field

[0001] The present application relates to the field of computational mechanics, and in particular to an isogeometric transient temperature field analysis method integrating birth-death unit technology. Background Art

[0002] Compared to traditional finite element analysis, isogeometric analysis directly utilizes non-uniform rational B-splines (NURBS) functions for physical modeling. Control points are automatically generated for the model, eliminating the need for complex and time-consuming meshing. Furthermore, due to the consistency between the geometric and analytical models and the high-order nature of NURBS basis functions, isogeometric analysis can achieve high-order continuity across the entire domain, resulting in higher accuracy and computational efficiency than finite element analysis.

[0003] Currently, temperature field analysis is mostly performed using finite element software, while isogeometric analysis remains largely a theoretical example. It is rarely used in problems involving complex load forms and computational domains with time-series requirements, such as dam concrete pouring. Therefore, a temperature field analysis method that considers isogeometric analysis is urgently needed to leverage its advantages in engineering problems. Summary of the Invention

[0004] The purpose of this application is to provide an isogeometric transient temperature field analysis method that integrates life and death unit technology, which solves the problem of difficulty in analyzing isogeometric transient temperature fields with complex load forms and time sequence requirements for the calculation domain.

[0005] To achieve the above objectives, this application provides the following solutions:

[0006] This application provides an isogeometric transient temperature field analysis method integrating birth-death unit technology, including:

[0007] Establish a NURBS model for isogeometric analysis and calculate the unit heat transfer matrix, unit thermal matrix and unit load matrix;

[0008] Determine whether the current calculation unit is in the calculation time domain, and process the unit heat transfer matrix, the unit heat melt matrix and the unit load array;

[0009] If not, set the unit heat transfer matrix and the unit load array to 0;

[0010] If yes, restore the loads corresponding to the unit heat transfer matrix and the unit load array, and remove the loads at the shared boundaries with the units in the calculation time domain in the unit load array and the unit heat transfer matrix;

[0011] Assembling the unit heat transfer matrix, the unit heat melt matrix and the unit load array into an overall matrix, and constructing a heat transfer equation according to the overall matrix;

[0012] The temperature of the control point is determined according to the heat transfer equation, and the temperature field of the solution domain is determined.

[0013] In one embodiment, using Determine the NURBS model; where χ is the geometric field; u(χ) is the physical field; R m is the NURBS basis function; m is the control point number; ξ represents the parameter coordinate; P m is the control point; N is the total number of control points; u m is the physical quantity at the control point;

[0014] According to the NURBS model, using Determine the unit heat transfer matrix; where, is the unit heat transfer matrix; k x is the heat transfer coefficient; R is the shape function matrix composed of NURBS basis functions; k y is the thermal conductivity coefficient; is the convective heat transfer coefficient between the object and the surrounding medium; To integrate the area within the cell range; is the boundary integration within the third type of boundary conditions; T represents the transposed matrix; x is the horizontal coordinate of the control point; y is the vertical coordinate of the control point; A e Indicates that the area is integrated within the cell range;

[0015] use Determine the unit heat-melting matrix; where, is the unit hot melt matrix; ρ is the material density; c T is the specific heat capacity;

[0016] use Determine the element load array; where, is the unit load array; Q is the internal heat source intensity of the object; is the boundary heat flux density; T ∞ is the external ambient temperature; It is the second type of boundary condition; It is the third type of boundary condition.

[0017] In one embodiment, the unit heat transfer matrix, the unit heat melt matrix and the unit load array are assembled into an integral matrix;

[0018] According to the central point difference method, using Construct the heat transfer equation of the overall matrix; where Δt is the time step; K T is the overall heat transfer matrix; CT is the overall heat-melting matrix; k is the time node; q k and q k+1 are the overall temperature arrays corresponding to time nodes k and k+1 respectively; and are the overall load arrays corresponding to time nodes k and k+1 respectively.

[0019] In one embodiment, a high-dimensional first conversion method is used to convert the two-dimensional index arrays of local control points and global control points into a one-dimensional index array;

[0020] Storing the mapping relationship of the one-dimensional index array into a new mapping index array;

[0021] The unit heat transfer matrix, the unit heat melt matrix and the unit load array are assembled into an overall matrix according to the new mapping index array.

[0022] In one embodiment, using θ(τ)=θ0(1-e -cτ ), determine the temperature rise function of concrete; where θ(τ) is the expression of the temperature rise function of concrete; θ0 is the final adiabatic temperature rise of concrete; c is a constant related to the type of cement in concrete and the amount of cement per cubic meter; τ is the calculation time point.

[0023] In one embodiment, a visualization network is constructed based on the NURBS model;

[0024] Converting the temperature value at the control point into the temperature of the vertex position of the visualization grid according to the shape function matrix and the temperature array of the control point;

[0025] The temperature values ​​at the vertex positions of the visualization grid are extracted and mapped to the range corresponding to the linear color gradient to determine the temperature field of the solution domain.

[0026] According to the specific embodiments provided in this application, this application discloses the following technical effects:

[0027] The present application provides an isogeometric transient temperature field analysis method that integrates life and death unit technology to determine whether the current computing unit is in the computing time domain; if not in the computing time domain, the unit heat transfer matrix and the unit load array are set to 0; if in the computing time domain, the loads corresponding to the unit heat transfer matrix and the unit load array are restored, and the loads at the shared boundary between the unit and other units in the computing time domain are removed, thereby realizing the analysis of the isogeometric transient temperature field of temperature load problems with timing requirements. The present application considers the implementation of the isogeometric transient temperature field analysis method under complex temperature load conditions, and promotes the application of isogeometric analysis in engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0029] Figure 1 Schematic diagram of the flow of an isogeometric transient temperature field analysis method integrating birth-death unit technology in one embodiment of the present application.

[0030] Figure 2 A schematic diagram of an isogeometric discrete model provided in one embodiment of the present application.

[0031] Figure 3 A schematic diagram of the birth and death unit processing flow provided in one embodiment of the present application.

[0032] Figure 4 A schematic diagram of the visualization process of isogeometric analysis provided in one embodiment of the present application.

[0033] Figure 5 A schematic diagram of the temperature field calculation results provided in one embodiment of the present application.

[0034] Figure 6 A schematic diagram of the calculation process of the isogeometric transient temperature field provided in one embodiment of the present application. DETAILED DESCRIPTION

[0035] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0036] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0037] The purpose of this application is to propose an isogeometric transient temperature field analysis method that integrates birth and death unit technology, establishes a geometric discrete model of foundation and multi-layer concrete that can automatically generate control points without meshing, and applies birth and death unit technology to simulate the concrete pouring process, which can improve modeling and calculation efficiency and achieve more efficient temperature field solution.

[0038] like Figure 1 As shown, an embodiment of the present application provides an isogeometric transient temperature field analysis method integrating birth and death unit technology, the specific contents of which are described as follows.

[0039] S1: Establish a NURBS model for isogeometric analysis and calculate the unit heat transfer matrix, unit thermal matrix and unit load matrix.

[0040] S2: Determine whether the current calculation unit is in the calculation time domain, and process the unit heat transfer matrix, the unit heat melt matrix and the unit load array.

[0041] S3: If not, set the unit heat transfer matrix and the unit load array to 0.

[0042] S4: If yes, restore the loads corresponding to the unit heat transfer matrix and the unit load array, and remove the loads at the shared boundaries with the units in the calculation time domain in the unit load array and the unit heat transfer matrix.

[0043] S5: Assembling the unit heat transfer matrix, the unit thermal melt matrix and the unit load array into an overall matrix, and constructing a heat transfer equation according to the overall matrix.

[0044] S6: Determine the temperature of the control point according to the heat transfer equation, and determine the temperature field of the solution domain.

[0045] Further, in an exemplary embodiment, S1 may be replaced by the following steps.

[0046] S101: Exploitation Determine the NURBS model; where χ is the geometric field; u(χ) is the physical field; R m is the NURBS basis function; m is the control point number; ξ represents the parameter coordinate; P m is the control point; N is the total number of control points; u m is the physical quantity at the control point.

[0047] like Figure 2 As shown in the figure, a geometric discrete model of the foundation and concrete is established. The model consists of 8 patches, 162 elements, 290 control points, 18 free boundaries, and 7 shared boundaries. The model materials include the foundation and RCC. The different NURBS patches are numbered to facilitate subsequent assembly matrix and birth / death element operations.

[0048] S102: Based on the NURBS model, use Determine the unit heat transfer matrix; where, is the unit heat transfer matrix; k x is the heat transfer coefficient; R is the shape function matrix composed of NURBS basis functions; k y is the thermal conductivity coefficient; is the convective heat transfer coefficient between the object and the surrounding medium; To integrate the area within the cell range; is the boundary integration within the third type of boundary conditions; T represents the transposed matrix; x is the horizontal coordinate of the control point; y is the vertical coordinate of the control point; A e Indicates whether to integrate the area within the cell range.

[0049] Among them, k x 、k y is the thermal conductivity coefficient, the unit is W / (m·K); ρ is the material density, the unit is kg / m 3 ;c T is the specific heat capacity, the unit is J / (kg·℃); Q is the internal heat source intensity of the object, the unit is W / kg; is the boundary heat flux density, in W / m 2 ; is the convection heat transfer coefficient between the object and the surrounding medium, with the unit of W / (m 2 ·K); T ∞ is the external environment temperature in °C.

[0050] S103: Exploit Determine the unit heat-melting matrix; where, is the unit hot melt matrix; ρ is the material density; c T is the specific heat capacity.

[0051] S104: Exploitation Determine the element load array; where, is the unit load array; Q is the internal heat source intensity of the object; is the boundary heat flux density; T ∞ is the external ambient temperature; It is the second type of boundary condition; It is the third type of boundary condition.

[0052] The birth and death element method is used to deal with the timing problem in the transient heat transfer process. The specific operation is: for the unit outside the calculation time domain, its heat transfer matrix is ​​set to 0, and all loads on the unit boundary are removed, that is, the unit is "killed". When the unit calculation time is reached, the heat transfer matrix and the corresponding load are restored, and the load at the boundary shared by the unit and the previous unit is removed to achieve "activation" of the unit.

[0053] like Figure 3 As shown, further, in an exemplary embodiment, S5 can be replaced by the following steps.

[0054] S501: Assembling the unit heat transfer matrix, the unit heat melt matrix and the unit load array into an integral matrix.

[0055] S502: According to the central point difference method, use Construct the heat transfer equation of the overall matrix; where Δt is the time step; K T is the overall heat transfer matrix; C T is the overall heat-melting matrix; k is the time node; q k and q k+1 are the overall temperature arrays corresponding to time nodes k and k+1 respectively; and are the overall load arrays corresponding to time nodes k and k+1 respectively.

[0056] Furthermore, S501 specifically includes:

[0057] S5011: Use the high-dimensional priority conversion method to convert the two-dimensional index arrays of local control points and global control points into one-dimensional index arrays.

[0058] S5012: Store the mapping relationship of the one-dimensional index array into a new mapping index array.

[0059] S5013: Assemble the unit heat transfer matrix, the unit thermal melt matrix and the unit load array into an overall matrix according to the new mapping index array.

[0060] The assembly process of the unit matrix adopts the "high-dimensional first" conversion method, which converts the two-dimensional index arrays of the control points in the local unit and the overall control points into two one-dimensional index arrays, stores the mapping relationship between the two one-dimensional arrays in a new mapping array, and assembles the unit matrix to the whole through the mapping array.

[0061] The element matrix is ​​calculated and assembled, during which the killed concrete material elements are "activated" one by one in order from bottom to top.

[0062] Furthermore, before S501, the following is also included:

[0063] Using θ(τ)=θ0(1-e -cτ ), determine the temperature rise function of concrete; where θ(τ) is the expression of the temperature rise function of concrete; θ0 is the final adiabatic temperature rise of concrete; c is a constant related to the type of cement in concrete and the amount of cement per cubic meter; τ is the calculation time point.

[0064] Set the time step and boundary conditions. Take the convection heat transfer boundary condition on the foundation surface, the adiabatic boundary condition on the bottom and both sides, the convection heat transfer boundary condition on the outer surface of the concrete block, and the hydration heat inside. The adiabatic temperature rise of the concrete is fitted according to the exponential function. In this application, θ0 is taken as 23°C, m is taken as 0.4, the initial temperature of the concrete is taken as 12°C, and the external temperature and the initial temperature of the foundation are taken as 5°C.

[0065] like Figure 5 and Figure 6As shown in the figure, the control point temperature is obtained by solving the heat transfer equation. The temperature field of the entire solution domain is calculated based on the control point temperature. It can be clearly seen that the temperature of the concrete block increases from bottom to top and the stratification is obvious. The highest temperature calculated by the structure gradually approaches the initial temperature of the concrete + the adiabatic temperature rise. The temperature at the junction of the foundation and the concrete gradually increases, which is in line with the theoretical law and proves the reliability of the calculation results.

[0066] Further, in an exemplary embodiment, S6 may be replaced by the following steps.

[0067] S601: Construct a visualization network based on the NURBS model.

[0068] S602: Converting the temperature value at the control point into the temperature of the vertex position of the visualization grid according to the shape function matrix and the temperature array of the control point.

[0069] S603: Extracting the temperature values ​​of the visual grid vertex positions, mapping the temperature values ​​to a range corresponding to the linear color gradient, and determining the temperature field of the solution domain.

[0070] like Figure 4 As shown in the figure, since the control points in isogeometric analysis are usually not located on the physical model, the temperatures at the control points need to be processed to obtain the temperature field of the solution domain. The specific operation is as follows: first, a visualization mesh is constructed based on the NURBS surface. Then, the temperature values ​​at the control points are converted into the temperatures at the mesh vertex positions using the shape function matrix and the control point temperature array. After extracting the mesh vertex data, the data is mapped to the range corresponding to the linear color gradient to obtain the temperature field cloud map.

[0071] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0072] This document uses specific examples to illustrate the principles and implementation methods of this application. The description of the above examples is only intended to help understand the method and core concept of this application. At the same time, for those skilled in the art, based on the concept of this application, there may be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A method for analyzing isogeometric transient temperature fields integrating birth-death unit technology, characterized in that: include: Establish a NURBS model for isogeometric analysis and calculate the unit heat transfer matrix, unit thermal matrix and unit load matrix; Determine whether the current calculation unit is in the calculation time domain, and process the unit heat transfer matrix, the unit heat melt matrix and the unit load array; If not, set the unit heat transfer matrix and the unit load array to 0; If yes, restore the loads corresponding to the unit heat transfer matrix and the unit load array, and remove the loads at the shared boundaries with the units in the calculation time domain in the unit load array and the unit heat transfer matrix; Assembling the unit heat transfer matrix, the unit heat melt matrix and the unit load array into an overall matrix, and constructing a heat transfer equation according to the overall matrix; The temperature of the control point is determined according to the heat transfer equation, and the temperature field of the solution domain is determined.

2. The isogeometric transient temperature field analysis method integrating the birth-death unit technology according to claim 1 is characterized in that: Establish a NURBS model for isogeometric analysis and calculate the unit heat transfer matrix, unit thermal matrix, and unit load matrix, including: use Determine the NURBS model; where χ is the geometric field; u(χ) is the physical field; R m is the NURBS basis function; m is the control point number; ξ represents the parameter coordinate; P m is the control point; N is the total number of control points; u m is the physical quantity at the control point; According to the NURBS model, using Determine the unit heat transfer matrix; where, is the unit heat transfer matrix; k x is the heat transfer coefficient; R is the shape function matrix composed of NURBS basis functions; k y is the thermal conductivity coefficient; is the convective heat transfer coefficient between the object and the surrounding medium; To integrate the area within the cell range; is the boundary integration within the third type of boundary conditions; T represents the transposed matrix; x is the horizontal coordinate of the control point; y is the vertical coordinate of the control point; A e Indicates that the area is integrated within the cell range; use Determine the unit heat-melting matrix; where, is the unit hot melt matrix; ρ is the material density; c T is the specific heat capacity; use Determine the element load array; where, is the unit load array; Q is the internal heat source intensity of the object; is the boundary heat flux density; T ∞ is the external ambient temperature; It is the second type of boundary condition; It is the third type of boundary condition.

3. The isogeometric transient temperature field analysis method integrating the birth-death unit technology according to claim 1 is characterized in that: Assembling the unit heat transfer matrix, the unit heat melt matrix, and the unit load array into an overall matrix, and constructing a heat transfer equation based on the overall matrix, specifically including: Assembling the unit heat transfer matrix, the unit heat melting matrix and the unit load array into an integral matrix; According to the central point difference method, using Construct the heat transfer equation of the overall matrix; where Δt is the time step; K T is the overall heat transfer matrix; C T is the overall heat-melting matrix; k is the time node; q k and q k+1 are the overall temperature arrays corresponding to time nodes k and k+1 respectively; and are the overall load arrays corresponding to time nodes k and k+1 respectively.

4. The isogeometric transient temperature field analysis method integrating the birth-death unit technology according to claim 3 is characterized in that: Assembling the unit heat transfer matrix, the unit heat melt matrix and the unit load array into an integral matrix specifically includes: The high-dimensional priority conversion method is used to convert the two-dimensional index arrays of local control points and global control points into one-dimensional index arrays; Storing the mapping relationship of the one-dimensional index array into a new mapping index array; The unit heat transfer matrix, the unit heat melt matrix and the unit load array are assembled into an overall matrix according to the new mapping index array.

5. The isogeometric transient temperature field analysis method integrating the birth-death unit technology according to claim 3 is characterized in that: Assembling the unit heat transfer matrix, the unit heat melt matrix and the unit load array into an integral matrix, further comprising: Using θ(τ)=θ0(1-e -cτ ), determine the temperature rise function of concrete; where θ(τ) is the expression of the temperature rise function of concrete; θ0 is the final adiabatic temperature rise of concrete; c is a constant related to the type of cement in concrete and the amount of cement per cubic meter; τ is the calculation time point.

6. The isogeometric transient temperature field analysis method integrating the birth-death unit technology according to claim 2 is characterized in that: Determine the temperature of the control point according to the heat transfer equation, and determine the temperature field of the solution domain, specifically including: Construct a visualization network based on the NURBS model; Converting the temperature value at the control point into the temperature of the vertex position of the visualization grid according to the shape function matrix and the temperature array of the control point; The temperature values ​​at the vertex positions of the visualization grid are extracted and mapped to the range corresponding to the linear color gradient to determine the temperature field of the solution domain.

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