Finite element analysis method, device, equipment and storage medium for stiffening rib plate unit

Abstract

The present invention discloses a finite element analysis method, apparatus, equipment, and storage medium for stiffening plate units, relating to the field of finite element analysis and calculation. The method includes establishing a local coordinate system oxyz of the plate unit with the mid-surface of the stiffening plate unit as a reference; calculating the plane equivalent thickness and bending equivalent thickness of the stiffening plate unit in the x-axis and y-axis directions; calculating the plane stress unit elastic modulus and the bending plate unit elastic modulus of the stiffening plate unit in the x-axis and y-axis directions to construct a plane stress unit elastic matrix and a bending plate unit elastic matrix; and constructing a plane stress unit stiffness matrix and a bending plate unit stiffness matrix based on the plane stress unit elastic matrix and the bending plate unit elastic matrix to calculate the internal forces and stresses of the plane stress unit and the bending plate unit. The present application can accurately and efficiently perform finite element analysis of stiffening plate units, meeting engineering requirements.

Description

Technical Field

[0001] The present application relates to the field of finite element analysis and calculation, and specifically to a finite element analysis method, device, equipment and storage medium for a stiffening rib plate unit. Background Art

[0002] Currently, in finite element analysis, due to the lack of specialized stiffening plate elements for orthogonal special-shaped plate analysis, engineers often use the following simulation strategies for finite element analysis:

[0003] (1) Fine plate element simulation: Both the panels and stiffeners are simulated using plate elements. This simulation method is closest to the actual situation. However, for long-span bridges with a large number of stiffeners, this simulation method significantly increases the modeling complexity and calculation time. In particular, when making design adjustments, the difficulty and workload of model modification will also increase significantly.

[0004] (2) Equivalent in-plane and out-of-plane thickness: This simulation method ignores the structural characteristics of the orthotropic plate and simply extends the in-plane thickness and out-of-plane thickness in the stiffening rib direction to the direction perpendicular to the stiffening rib. Since the stiffness of the plate and shell elements in the two directions affect each other, the stiffness of the orthotropic plate element is exaggerated in the calculation, and the structural characteristics in the direction perpendicular to the stiffening rib are artificially strengthened, resulting in the structural stiffness of the orthotropic plate being larger than the actual value and the calculated deformation being smaller, making the calculation result unsafe and affecting the safety assessment of the structure.

[0005] (3) Grid method: This simulation method concentrates the bending and torsional stiffness of the panel and stiffeners in the adjacent equivalent grids, where the longitudinal stiffness is concentrated in the longitudinal grids and the transverse stiffness is concentrated in the transverse grids. To achieve higher calculation accuracy, the grids need to be divided densely enough, which not only increases the workload of modeling but also limits the flexible adjustment of the design scheme.

[0006] Therefore, in view of the problems of complex simulation methods and low calculation accuracy in the current finite element analysis of stiffening rib plate units, how to accurately and efficiently implement the finite element analysis of stiffening rib plate units has become an urgent problem to be solved. Summary of the Invention

[0007] The present application provides a finite element analysis method, device, equipment and storage medium for stiffening rib plate units, which can accurately and efficiently perform finite element analysis of stiffening rib plate units to meet engineering requirements.

[0008] In a first aspect, an embodiment of the present application provides a finite element analysis method for a stiffening rib plate unit, the finite element analysis method for a stiffening rib plate unit comprising:

[0009] The local coordinate system oxyz of the plate element is established with the mid-surface of the stiffened plate element as the reference, where the oxy plane is located at the mid-surface of the plate, the z axis is perpendicular to the plate plane, the longitudinal stiffeners of the stiffened plate element are along the x-axis direction of the coordinate system, and the transverse stiffeners are along the y-axis direction of the coordinate system;

[0010] The plane equivalent thickness and bending equivalent thickness of the stiffening rib plate element in the x-axis direction, as well as the plane equivalent thickness and bending equivalent thickness in the y-axis direction are calculated respectively;

[0011] Based on the calculated plane equivalent thickness and bending equivalent thickness, the elastic modulus of the plane stress unit and the elastic modulus of the bending plate unit in the x-axis and y-axis directions of the stiffening rib plate unit are calculated to construct the plane stress unit elastic matrix and the bending plate unit elastic matrix;

[0012] According to the plane stress unit elastic matrix and the bending plate unit elastic matrix, the plane stress unit stiffness matrix and the bending plate unit stiffness matrix are constructed to realize the calculation of the internal force and stress of the plane stress unit and the bending plate unit.

[0013] In combination with the first aspect, in one embodiment, respectively calculating the planar equivalent thickness and bending equivalent thickness of the stiffening rib plate element in the x-axis direction, and the planar equivalent thickness and bending equivalent thickness in the y-axis direction, specifically includes:

[0014] Calculate the equivalent thickness of the stiffener plate element in the x-axis direction. Specifically,

[0015]

[0016] in, represents the equivalent thickness of the stiffening plate element in the x-axis direction. represents the top plate thickness of the stiffener plate element, represents the area of ​​a single longitudinal stiffener in the stiffened plate element, Indicates the distance between two adjacent longitudinal stiffeners in the stiffener plate element;

[0017] Obtain the position of the centroid of the equivalent section formed between the top plate of the stiffening rib plate unit and the longitudinal stiffener, and record the equivalent section as the first equivalent section, and then calculate the distance from the upper edge of the first equivalent section to the centroid of the first equivalent section , and the distance between the lower edge of the first equivalent section and the centroid of the first equivalent section ;

[0018] Calculate the equivalent thickness of the stiffener plate element in the y-axis direction. Specifically,

[0019]

[0020] in, represents the equivalent thickness of the stiffening plate element in the y-axis direction. represents the area of ​​a single transverse stiffener in the stiffened plate element, Indicates the distance between two adjacent transverse stiffeners in the stiffener plate element;

[0021] Obtain the position of the centroid of the equivalent section formed between the top plate of the stiffening rib plate unit and the transverse stiffener, and record the equivalent section as the second equivalent section, and then calculate the distance from the upper edge of the second equivalent section to the centroid of the second equivalent section , and the distance between the lower edge of the second equivalent cross section and the centroid of the second equivalent cross section ;

[0022] Calculate the bending equivalent thickness of the stiffener plate element in the x-axis direction. Specifically,

[0023]

[0024] in, represents the bending equivalent thickness of the stiffening rib plate element in the x-axis direction, represents the transverse bending inertia moment of the top plate of the stiffened rib plate element relative to the centroid of the first equivalent section, Represents the transverse bending inertia moment of the longitudinal stiffener of the stiffened plate element relative to the centroid of the first equivalent section;

[0025] Calculate the bending equivalent thickness of the stiffener plate element in the y-axis direction. Specifically,

[0026]

[0027] in, represents the bending equivalent thickness of the stiffener plate element in the y-axis direction, represents the transverse bending inertia moment of the top plate of the stiffened rib plate element relative to the centroid of the second equivalent section, Represents the transverse bending moment of inertia of the transverse stiffener of the stiffened plate element relative to the centroid of the second equivalent cross section.

[0028] In combination with the first aspect, in one embodiment, the calculation of the plane stress unit elastic modulus and the bending plate unit elastic modulus of the stiffening rib plate unit in the x-axis direction and the y-axis direction is performed, wherein:

[0029] For the plane stress element elastic modulus of the stiffening rib plate element in the x-axis direction, specifically,

[0030]

[0031] in, represents the plane stress element elastic modulus of the stiffening rib plate element in the x-axis direction, represents the material elastic modulus of the stiffener plate element, represents the equivalent thickness of the stiffening plate element in the x-axis direction. Indicates the top plate thickness of the stiffener plate element;

[0032] For the elastic modulus of the bending plate element of the stiffening rib plate element in the x-axis direction, specifically,

[0033]

[0034] in, represents the elastic modulus of the stiffening plate element in the x-axis direction, represents the bending equivalent thickness of the stiffener plate element in the x-axis direction;

[0035] For the plane stress element elastic modulus of the stiffening rib plate element in the y-axis direction, specifically,

[0036]

[0037] in, represents the plane stress element elastic modulus of the stiffening rib plate element in the y-axis direction, It represents the equivalent thickness of the stiffener plate element in the y-axis direction;

[0038] For the elastic modulus of the stiffening plate element in the y-axis direction, specifically,

[0039]

[0040] in, represents the elastic modulus of the stiffening plate element in the y-axis direction. It represents the bending equivalent thickness of the stiffener plate element in the y-axis direction.

[0041] In combination with the first aspect, in one embodiment, the plane stress unit elastic matrix and the bending plate unit elastic matrix are constructed, wherein:

[0042] The plane stress unit elastic matrix is ​​specifically:

[0043]

[0044] in, represents the plane stress element elastic matrix, represents the plane stress element elastic modulus of the stiffening rib plate element in the x-axis direction, Indicates the intermediate quantity, , 、 Both represent intermediate quantities. , represents the material elastic modulus of the stiffener plate element, represents the plane stress element elastic modulus of the stiffening rib plate element in the y-axis direction, represents the Poisson's ratio of the stiffener plate element, , represents the material shear modulus of the stiffener plate element;

[0045] The elastic matrix of the bending plate unit is specifically:

[0046]

[0047] in, represents the elastic matrix of the bending plate element, represents the top plate thickness of the stiffener plate element, represents the elastic modulus of the stiffening plate element in the x-axis direction, Represents the elastic modulus of the stiffener plate element in the y-axis direction.

[0048] In combination with the first aspect, in one embodiment, the plane stress unit stiffness matrix and the bending plate unit stiffness matrix are constructed, wherein:

[0049] The plane stress unit stiffness matrix is ​​specifically:

[0050]

[0051] in, represents the plane stress element stiffness matrix, represents the top plate thickness of the stiffener plate element, represents the strain matrix of the plane stress element, represents the matrix transpose, represents the plane stress element elastic matrix, The area domain representing the stiffener plate element surface;

[0052] The bending plate element stiffness matrix is ​​specifically:

[0053]

[0054] in, represents the stiffness matrix of the bending plate element, represents the strain matrix of the bending plate element, represents the elastic matrix of the bent plate element.

[0055] In conjunction with the first aspect, in one embodiment, the calculation of the internal forces and stresses of the plane stress unit and the curved plate unit is implemented, wherein the calculation of the internal forces and stresses of the plane stress unit specifically includes:

[0056] Calculate the stress of a plane stress element. Specifically,

[0057]

[0058] in, represents the stress of the plane stress element, represents the top plate thickness of the stiffener plate element, represents the equivalent thickness of the stiffening plate element in the x-axis direction. represents the equivalent thickness of the stiffening plate element in the y-axis direction. represents the plane stress element elastic matrix, represents the element strain, , represents the strain matrix of the plane stress element, represents the unit displacement, , represents the matrix transpose, Represents the nodes in the stiffener plate element The displacement along the x-axis, Represents the nodes in the stiffener plate element Displacement along the y-axis;

[0059] Calculate the internal forces per unit width of a plane stress element. Specifically,

[0060]

[0061] in, represents the internal force per unit width of the plane stress element, represents the equivalent thickness of the stiffening plate element in the x-axis direction. Represents the plane equivalent thickness of the stiffener plate element in the y-axis direction.

[0062] In conjunction with the first aspect, in one embodiment, the calculation of the internal forces and stresses of the plane stress unit and the curved plate unit is implemented, wherein the calculation of the internal forces and stresses of the curved plate unit specifically includes:

[0063] Calculate the internal forces per unit width of the curved plate element. Specifically,

[0064]

[0065] in, represents the internal force per unit width of the bending plate element, represents the elastic matrix of the bending plate element, represents the strain matrix of the bending plate element, represents unit displacement, , represents the matrix transpose, Represents the nodes in the stiffener plate element The deflection along the z-axis is, Represents the nodes in the stiffener plate element The rotation angle around the x-axis, Represents the nodes in the stiffener plate element The rotation angle around the y-axis at ;

[0066] Calculate the stress of the curved plate element. Specifically,

[0067]

[0068] in, represents the stress of the bending plate element, It represents the z-axis coordinate of the stress calculation point of the stiffening plate element in the direction of equivalent thickness in the x-axis direction, and the z-axis coordinate value of the top surface of the stiffening plate element in the direction of equivalent thickness in the x-axis direction is equal to The z-axis coordinate value of the bottom surface of the stiffening rib plate element in the equivalent thickness direction of the x-axis direction is equal to , It represents the z-axis coordinate of the stiffening plate element in the equivalent thickness direction of the y-axis, and the z-axis coordinate value of the top surface of the stiffening plate element in the equivalent thickness direction of the y-axis is equal to The z-axis coordinate value of the bottom surface of the stiffening rib plate element in the equivalent thickness direction in the y-axis direction is equal to , The z-axis coordinate of the shear stress thickness direction of the stiffening plate element is equal to , the z-axis coordinate value of the shear stress thickness direction of the bottom surface of the stiffening rib plate element is equal to , Indicates the top plate thickness of the stiffener plate element.

[0069] In a second aspect, an embodiment of the present application provides a finite element analysis device for a stiffening rib plate unit, the finite element analysis device for a stiffening rib plate unit comprising:

[0070] Create a module for establishing the local coordinate system oxyz of the plate element based on the mid-surface of the stiffened plate element, where the oxy plane is located at the mid-surface of the plate, the z axis is perpendicular to the plate plane, the longitudinal stiffeners of the stiffened plate element are along the x-axis direction of the coordinate system, and the transverse stiffeners are along the y-axis direction of the coordinate system;

[0071] a calculation module, which is used to respectively calculate the plane equivalent thickness and bending equivalent thickness of the stiffening rib plate unit in the x-axis direction, as well as the plane equivalent thickness and bending equivalent thickness in the y-axis direction, and calculate the plane stress unit elastic modulus and the bending plate unit elastic modulus of the stiffening rib plate unit in the x-axis direction and the y-axis direction based on the calculated plane equivalent thickness and bending equivalent thickness, so as to construct the plane stress unit elastic matrix and the bending plate unit elastic matrix;

[0072] An execution module is used to construct a plane stress unit stiffness matrix and a bending plate unit stiffness matrix according to the plane stress unit elastic matrix and the bending plate unit elastic matrix, so as to realize the internal force and stress calculation of the plane stress unit and the bending plate unit.

[0073] In a third aspect, an embodiment of the present application provides a stiffening rib plate unit finite element analysis device, which includes a processor, a memory, and a stiffening rib plate unit finite element analysis program stored in the memory and executable by the processor, wherein when the stiffening rib plate unit finite element analysis program is executed by the processor, the steps of the stiffening rib plate unit finite element analysis method described above are implemented.

[0074] In a fourth aspect, an embodiment of the present application provides a computer-readable storage medium, on which a finite element analysis program for a stiffening rib plate unit is stored, wherein when the finite element analysis program for a stiffening rib plate unit is executed by a processor, the steps of the finite element analysis method for a stiffening rib plate unit described above are implemented.

[0075] The beneficial effects of the technical solutions provided in the embodiments of the present application include:

[0076] The characteristics of orthotropic materials are used to realize the different properties of the longitudinal and transverse stiffeners of the stiffening slab. For the stiffening slab unit composed of two parts, the plane stress unit and the bending plate unit, the plane tension and compression equivalent plate thickness and the bending equivalent plate thickness of the stiffening slab unit in the x-axis direction and y-axis direction of the local coordinate system of the plate unit are calculated respectively. According to the different equivalent plate thicknesses, the stiffness matrix, internal force and stress calculation equations are modified respectively, and then the stiffening slab unit model considering the structural characteristics of the orthotropic plate is obtained, and the finite element analysis of the stiffening slab unit is realized accurately and efficiently to meet the engineering needs. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 This is a flow chart of the finite element analysis method for stiffened rib plate elements in this application;

[0078] Figure 2 It is the structural diagram of the stiffening rib plate unit;

[0079] Figure 3This is a schematic diagram of the functional modules of the finite element analysis device for stiffening rib plate units in this application;

[0080] Figure 4 Schematic diagram of the hardware structure of the finite element analysis equipment for the stiffening plate unit in this application. DETAILED DESCRIPTION

[0081] In order to enable those skilled in the art to better understand the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. 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 this application.

[0082] In order to make the objectives, technical solutions and advantages of this application clearer, the implementation methods of this application will be further described in detail below with reference to the accompanying drawings.

[0083] In a first aspect, an embodiment of the present application provides a finite element analysis method for a stiffening rib plate unit.

[0084] In one embodiment, referring to Figure 1 , Figure 1 This is a flow chart of the finite element analysis method for stiffening plate elements in this application. Figure 1 As shown in Figure 2, the finite element analysis method for stiffened rib plate elements includes:

[0085] S1: Establish the local coordinate system oxyz of the plate element with the mid-surface of the stiffened plate element as the reference, where the oxy plane is located at the mid-surface of the plate, the z axis is perpendicular to the plate plane, the longitudinal stiffeners of the stiffened plate element are along the x-axis direction of the coordinate system, and the transverse stiffeners are along the y-axis direction of the coordinate system;

[0086] See Figure 2 As shown, the coordinate system is established with the direction of the longitudinal stiffening ribs of the stiffening rib plate unit as the x-axis direction, the direction of the transverse stiffening ribs of the stiffening rib plate unit as the y-axis direction, and the direction perpendicular to the plane of the stiffening rib plate unit as the z-axis direction;

[0087] S2: Calculate the equivalent thickness of the stiffener plate element in the x-axis direction and the equivalent thickness of the stiffener plate element in the y-axis direction;

[0088] S3: Based on the calculated plane equivalent thickness and bending equivalent thickness, the elastic modulus of the plane stress element and the elastic modulus of the bending plate element in the x-axis and y-axis directions of the stiffening plate element are calculated to construct the plane stress element elastic matrix and the bending plate element elastic matrix; the stiffening plate element is composed of plane stress elements and bending plate elements, and the bending plate element is a unit based on Kirchhoff theory;

[0089] S4: Based on the plane stress unit elastic matrix and the bending plate unit elastic matrix, construct the plane stress unit stiffness matrix and the bending plate unit stiffness matrix to realize the internal force and stress calculation of the plane stress unit and the bending plate unit.

[0090] Furthermore, in one embodiment, the planar equivalent thickness and bending equivalent thickness of the stiffening rib plate element in the x-axis direction, as well as the planar equivalent thickness and bending equivalent thickness in the y-axis direction, are calculated, specifically including:

[0091] S201: Calculate the equivalent thickness of the stiffener plate element in the x-axis direction. Specifically,

[0092]

[0093] in, represents the equivalent thickness of the stiffening plate element in the x-axis direction. represents the top plate thickness of the stiffener plate element, represents the area of ​​a single longitudinal stiffener in the stiffened plate element, Indicates the distance between two adjacent longitudinal stiffeners in the stiffener plate element;

[0094] S202: Obtain the position of the centroid of the equivalent section formed between the top plate of the stiffening rib plate unit and the longitudinal stiffening rib, and record the equivalent section as the first equivalent section, and then calculate the distance between the upper edge of the first equivalent section and the centroid of the first equivalent section , and the distance between the lower edge of the first equivalent section and the centroid of the first equivalent section ;

[0095] S203: Calculate the equivalent thickness of the stiffening plate element in the y-axis direction. Specifically,

[0096]

[0097] in, represents the equivalent thickness of the stiffening plate element in the y-axis direction. represents the area of ​​a single transverse stiffener in the stiffened plate element, Indicates the distance between two adjacent transverse stiffeners in the stiffener plate element;

[0098] S204: Obtain the position of the centroid of the equivalent section formed between the top plate of the stiffening rib plate unit and the transverse stiffening rib, and record the equivalent section as the second equivalent section, and then calculate the distance between the upper edge of the second equivalent section and the centroid of the second equivalent section , and the distance between the lower edge of the second equivalent cross section and the centroid of the second equivalent cross section ;

[0099] S205: Calculate the bending equivalent thickness of the stiffener plate element in the x-axis direction. Specifically,

[0100]

[0101] in, represents the bending equivalent thickness of the stiffening rib plate element in the x-axis direction, represents the transverse bending inertia moment of the top plate of the stiffened rib plate element relative to the centroid of the first equivalent section, Represents the transverse bending inertia moment of the longitudinal stiffener of the stiffened plate element relative to the centroid of the first equivalent section;

[0102] S206: Calculate the bending equivalent thickness of the stiffening plate element in the y-axis direction. Specifically,

[0103]

[0104] in, represents the bending equivalent thickness of the stiffener plate element in the y-axis direction, represents the transverse bending inertia moment of the top plate of the stiffened rib plate element relative to the centroid of the second equivalent section, Represents the transverse bending moment of inertia of the transverse stiffener of the stiffened plate element relative to the centroid of the second equivalent cross section.

[0105] Furthermore, in one embodiment, the elastic modulus of the plane stress element and the elastic modulus of the bending plate element of the stiffening rib plate element in the x-axis direction and the y-axis direction are calculated, wherein:

[0106] For the plane stress element elastic modulus of the stiffening rib plate element in the x-axis direction, specifically,

[0107]

[0108] in, represents the plane stress element elastic modulus of the stiffening rib plate element in the x-axis direction, represents the material elastic modulus of the stiffener plate element, represents the equivalent thickness of the stiffening plate element in the x-axis direction. Indicates the top plate thickness of the stiffener plate element;

[0109] For the elastic modulus of the bending plate element of the stiffening rib plate element in the x-axis direction, specifically,

[0110]

[0111] in, represents the elastic modulus of the stiffening plate element in the x-axis direction, Indicates the bending equivalent thickness of the stiffening rib plate element in the x-axis direction; the bending plate element is a finite element element suitable for thin plate bending analysis;

[0112] For the plane stress element elastic modulus of the stiffening rib plate element in the y-axis direction, specifically,

[0113]

[0114] in, represents the plane stress element elastic modulus of the stiffening rib plate element in the y-axis direction, It represents the equivalent thickness of the stiffener plate element in the y-axis direction;

[0115] For the elastic modulus of the stiffening plate element in the y-axis direction, specifically,

[0116]

[0117] in, represents the elastic modulus of the stiffening plate element in the y-axis direction. It represents the bending equivalent thickness of the stiffener plate element in the y-axis direction.

[0118] Furthermore, in one embodiment, a plane stress unit elastic matrix and a bending plate unit elastic matrix are constructed, wherein:

[0119] The plane stress unit elastic matrix is ​​specifically:

[0120]

[0121] in, represents the plane stress element elastic matrix, represents the plane stress element elastic modulus of the stiffening rib plate element in the x-axis direction, Indicates the intermediate quantity, , 、 Both represent intermediate quantities. , represents the material elastic modulus of the stiffener plate element, represents the plane stress element elastic modulus of the stiffening rib plate element in the y-axis direction, represents the Poisson's ratio of the stiffener plate element, , represents the material shear modulus of the stiffener plate element;

[0122] The elastic matrix of the bending plate unit is specifically:

[0123]

[0124] in, represents the elastic matrix of the bending plate element, represents the top plate thickness of the stiffener plate element, represents the elastic modulus of the stiffening plate element in the x-axis direction, Represents the elastic modulus of the stiffener plate element in the y-axis direction.

[0125] Furthermore, in one embodiment, a plane stress unit stiffness matrix and a bending plate unit stiffness matrix are constructed, where:

[0126] The plane stress unit stiffness matrix is ​​specifically:

[0127]

[0128] in, represents the plane stress element stiffness matrix, represents the top plate thickness of the stiffener plate element, represents the strain matrix of the plane stress element, represents the matrix transpose, represents the plane stress element elastic matrix, The area domain representing the stiffener plate element surface;

[0129] The bending plate element stiffness matrix is ​​specifically:

[0130]

[0131] in, represents the stiffness matrix of the bending plate element, represents the strain matrix of the bending plate element, represents the elastic matrix of the bent plate element.

[0132] Furthermore, in one embodiment, the calculation of internal forces and stresses of plane stress elements and curved plate elements is implemented, wherein the calculation of internal forces and stresses of plane stress elements specifically includes:

[0133] S401: Calculate the stress of the plane stress element. Specifically,

[0134]

[0135] in, represents the stress of the plane stress element, represents the top plate thickness of the stiffener plate element, represents the equivalent thickness of the stiffening plate element in the x-axis direction. represents the equivalent thickness of the stiffening plate element in the y-axis direction. represents the plane stress element elastic matrix, represents the element strain, , represents the strain matrix of the plane stress element, represents the unit displacement, , represents the matrix transpose, Represents the nodes in the stiffener plate element The displacement along the x-axis, Represents the nodes in the stiffener plate element Displacement along the y-axis;

[0136] S402: Calculate the internal force per unit width of the plane stress element. Specifically,

[0137]

[0138] in, represents the internal force per unit width of the plane stress element, represents the equivalent thickness of the stiffening plate element in the x-axis direction. Represents the plane equivalent thickness of the stiffener plate element in the y-axis direction.

[0139] Furthermore, in one embodiment, the calculation of internal forces and stresses of plane stress elements and curved plate elements is implemented, wherein the calculation of internal forces and stresses of curved plate elements specifically includes:

[0140] S411: Calculate the internal force per unit width of the curved plate element. Specifically,

[0141]

[0142] in, represents the internal force per unit width of the bending plate element, represents the elastic matrix of the bending plate element, represents the strain matrix of the bending plate element, represents unit displacement, , represents the matrix transpose, Represents the nodes in the stiffener plate element The deflection along the z-axis is, Represents the nodes in the stiffener plate element The rotation angle around the x-axis, Represents the nodes in the stiffener plate element The rotation angle around the y-axis at ; It should be noted that the positive and negative signs of the internal moment per unit width are consistent with the positive and negative signs of the top plate stress of the equivalent plate unit, and the direction of the top plate stress is consistent with elastic mechanics (positive in the positive direction and negative in the negative direction);

[0143] S412: Calculate the stress of the curved plate element. Specifically,

[0144]

[0145] in, represents the stress of the bending plate element, It represents the z-axis coordinate of the stress calculation point of the stiffening plate element in the direction of equivalent thickness in the x-axis direction, and the z-axis coordinate value of the top surface of the stiffening plate element in the direction of equivalent thickness in the x-axis direction is equal to The z-axis coordinate value of the bottom surface of the stiffening rib plate element in the equivalent thickness direction of the x-axis direction is equal to , It represents the z-axis coordinate of the stiffening plate element in the equivalent thickness direction of the y-axis, and the z-axis coordinate value of the top surface of the stiffening plate element in the equivalent thickness direction of the y-axis is equal to The z-axis coordinate value of the bottom surface of the stiffening rib plate element in the equivalent thickness direction in the y-axis direction is equal to , The z-axis coordinate of the shear stress thickness direction of the stiffening plate element is equal to , the z-axis coordinate value of the shear stress thickness direction of the bottom surface of the stiffening rib plate element is equal to , Indicates the top plate thickness of the stiffener plate element.

[0146] The finite element analysis method of the stiffening rib plate unit in the embodiment of the present application adopts the characteristics of orthotropic materials to realize the different characteristics of the longitudinal and transverse stiffening ribs of the stiffening rib plate. For the stiffening rib plate unit composed of two parts, the plane stress unit and the bending plate unit, the plane stress unit is a four-node isoparametric unit. The plane tension and compression equivalent plate thickness and the bending equivalent plate thickness of the stiffening rib plate unit in the x-axis direction and the y-axis direction of the local coordinate system of the plate unit are calculated respectively. The stiffness matrix, internal force and stress calculation equations are corrected according to different equivalent plate thicknesses, and then a stiffening rib plate unit model that takes into account the structural characteristics of the orthotropic plate is obtained, so that the finite element analysis of the stiffening rib plate unit is accurately and efficiently realized to meet engineering needs.

[0147] In a second aspect, an embodiment of the present application further provides a finite element analysis device for a stiffening rib plate unit.

[0148] In one embodiment, referring to Figure 3 , Figure 3This is a schematic diagram of the functional modules of the finite element analysis device for stiffening rib plate units in this application. Figure 3 As shown, the finite element analysis device of the stiffening rib plate unit includes: a creation module, a calculation module, and an execution module.

[0149] The creation module is used to establish the local coordinate system oxyz of the plate unit based on the mid-surface of the stiffening rib plate unit, wherein the oxy plane is located at the mid-surface of the plate, the z axis is perpendicular to the plate plane, the longitudinal stiffeners of the stiffening rib plate unit are along the x-axis direction of the coordinate system, and the transverse stiffeners are along the y-axis direction of the coordinate system; the calculation module is used to respectively calculate the plane equivalent thickness and bending equivalent thickness of the stiffening rib plate unit in the x-axis direction, as well as the plane equivalent thickness and bending equivalent thickness in the y-axis direction, and based on the calculated plane equivalent thickness and bending equivalent thickness, calculate the plane stress unit elastic modulus and the bending plate unit elastic modulus of the stiffening rib plate unit in the x-axis direction and the y-axis direction to construct the plane stress unit elastic matrix and the bending plate unit elastic matrix; the execution module is used to construct the plane stress unit stiffness matrix and the bending plate unit stiffness matrix according to the plane stress unit elastic matrix and the bending plate unit elastic matrix to realize the internal force and stress calculation of the plane stress unit and the bending plate unit.

[0150] In a third aspect, an embodiment of the present application provides a stiffening plate unit finite element analysis device, which may be a personal computer (PC), a laptop computer, a server, or other device with data processing capabilities.

[0151] Reference Figure 4 , Figure 4 Schematic diagram of the hardware structure of the stiffening plate unit finite element analysis device involved in the embodiment of the present application. In the embodiment of the present application, the stiffening plate unit finite element analysis device may include a processor, a memory, a communication interface and a communication bus.

[0152] The communication bus may be of any type and is used to interconnect the processor, memory, and communication interface.

[0153] Communication interfaces include input / output (I / O), physical, and logical interfaces, which interconnect components within the finite element analysis system and other devices (such as other computing devices or user devices). Physical interfaces can be Ethernet, fiber, or ATM; user devices can be displays or keyboards.

[0154] The memory can be various types of storage media, such as random access memory (RAM), read-only memory (ROM), non-volatile RAM (NVRAM), flash memory, optical storage, hard disk, programmable ROM (PROM), erasable PROM (EPROM), electrically erasable PROM (EEPROM), etc.

[0155] The processor may be a general-purpose processor that can invoke a stiffening plate unit finite element analysis program stored in a memory and execute the stiffening plate unit finite element analysis method provided in the embodiments of the present application. For example, the general-purpose processor may be a central processing unit (CPU). The method executed when the stiffening plate unit finite element analysis program is invoked can be referenced from the various embodiments of the stiffening plate unit finite element analysis method of the present application and will not be further described here.

[0156] Those skilled in the art will understand that Figure 4 The hardware structure shown in the figure does not constitute a limitation to the present application and may include more or fewer components than shown in the figure, or a combination of certain components, or a different arrangement of components.

[0157] In a fourth aspect, an embodiment of the present application also provides a computer-readable storage medium.

[0158] The computer-readable storage medium of the present application stores a stiffening rib plate unit finite element analysis program, wherein when the stiffening rib plate unit finite element analysis program is executed by a processor, the steps of the stiffening rib plate unit finite element analysis method as described above are implemented.

[0159] Among them, the method implemented when the stiffening rib plate unit finite element analysis program is executed can refer to the various embodiments of the stiffening rib plate unit finite element analysis method of this application, and will not be repeated here.

[0160] The terms "including" and "having" and any variations thereof in the specification and claims of this application and the above-mentioned drawings are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not limited to the listed steps or units, but optionally includes steps or units that are not listed, or optionally includes other steps or units inherent to these processes, methods, products or devices. The terms "first", "second" and "third" are used to distinguish different objects, etc., and do not represent a sequence, nor do they limit the "first", "second" and "third" to different types.

[0161] In the description of the embodiments of this application, the words "exemplary," "for example," or "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary," "for example," or "for example" in the embodiments of this application should not be construed as being preferred or advantageous over other embodiments or designs. Rather, the use of words such as "exemplary," "for example," or "for example" is intended to present the relevant concepts in a concrete manner.

[0162] In the description of the embodiments of the present application, unless otherwise specified, “ / ” means or, for example, A / B can mean A or B; “and / or” in the text is merely a description of the association relationship of associated objects, indicating that three relationships may exist, for example, A and / or B can mean: A exists alone, A and B exist at the same time, and B exists alone. In addition, in the description of the embodiments of the present application, “multiple” refers to two or more than two.

[0163] In some processes described in the embodiments of the present application, multiple operations or steps are included that appear in a specific order. However, it should be understood that these operations or steps may not be performed in the order in which they appear in the embodiments of the present application or may be performed in parallel. The sequence numbers of the operations are only used to distinguish between different operations, and the sequence numbers themselves do not represent any order of execution. In addition, these processes may include more or fewer operations, and these operations or steps may be performed in sequence or in parallel, and these operations or steps may be combined.

[0164] Through the description of the above embodiments, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be implemented by means of software plus the 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 this application, or the part that contributes to the existing technology, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) as described above and includes a number of instructions for enabling a terminal device to execute the methods described in each embodiment of this application.

[0165] The above are only preferred embodiments of the present application and do not limit the patent scope of the present application. Any equivalent structure or equivalent process transformation made using the contents of the present application specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present application.

Claims

1. A finite element analysis method for stiffening rib plate unit, characterized in that: The stiffening rib plate unit finite element analysis method includes: The local coordinate system oxyz of the plate element is established with the mid-surface of the stiffened plate element as the reference, where the oxy plane is located at the mid-surface of the plate, the z axis is perpendicular to the plate plane, the longitudinal stiffeners of the stiffened plate element are along the x-axis direction of the coordinate system, and the transverse stiffeners are along the y-axis direction of the coordinate system; The plane equivalent thickness and bending equivalent thickness of the stiffening rib plate element in the x-axis direction, as well as the plane equivalent thickness and bending equivalent thickness in the y-axis direction are calculated respectively; Based on the calculated plane equivalent thickness and bending equivalent thickness, the elastic modulus of the plane stress unit and the elastic modulus of the bending plate unit in the x-axis and y-axis directions of the stiffening rib plate unit are calculated to construct the plane stress unit elastic matrix and the bending plate unit elastic matrix; Constructing a plane stress unit stiffness matrix and a bending plate unit stiffness matrix based on the plane stress unit elastic matrix and the bending plate unit elastic matrix to realize internal force and stress calculation of the plane stress unit and the bending plate unit; The calculation of the equivalent thickness and bending equivalent thickness of the stiffening plate element in the x-axis direction, and the equivalent thickness and bending equivalent thickness in the y-axis direction, respectively, specifically includes: Calculate the equivalent thickness of the stiffener plate element in the x-axis direction. Specifically, in, represents the equivalent thickness of the stiffening plate element in the x-axis direction. represents the top plate thickness of the stiffener plate element, represents the area of ​​a single longitudinal stiffener in the stiffened plate element, Indicates the distance between two adjacent longitudinal stiffeners in the stiffener plate element; Obtain the position of the centroid of the equivalent section formed between the top plate of the stiffening rib plate unit and the longitudinal stiffener, and record the equivalent section as the first equivalent section, and then calculate the distance from the upper edge of the first equivalent section to the centroid of the first equivalent section , and the distance between the lower edge of the first equivalent section and the centroid of the first equivalent section ; Calculate the equivalent thickness of the stiffener plate element in the y-axis direction. Specifically, in, represents the equivalent thickness of the stiffening plate element in the y-axis direction. represents the area of ​​a single transverse stiffener in the stiffened plate element, Indicates the distance between two adjacent transverse stiffeners in the stiffener plate element; Obtain the position of the centroid of the equivalent section formed between the top plate of the stiffening rib plate unit and the transverse stiffener, and record the equivalent section as the second equivalent section, and then calculate the distance from the upper edge of the second equivalent section to the centroid of the second equivalent section , and the distance between the lower edge of the second equivalent cross section and the centroid of the second equivalent cross section ; Calculate the bending equivalent thickness of the stiffener plate element in the x-axis direction. Specifically, in, represents the bending equivalent thickness of the stiffening rib plate element in the x-axis direction, represents the transverse bending inertia moment of the top plate of the stiffened rib plate element relative to the centroid of the first equivalent section, Represents the transverse bending inertia moment of the longitudinal stiffener of the stiffened plate element relative to the centroid of the first equivalent section; Calculate the bending equivalent thickness of the stiffener plate element in the y-axis direction. Specifically, in, represents the bending equivalent thickness of the stiffener plate element in the y-axis direction, represents the transverse bending inertia moment of the top plate of the stiffened rib plate element relative to the centroid of the second equivalent section, Represents the transverse bending moment of inertia of the transverse stiffener of the stiffened plate element relative to the centroid of the second equivalent cross section.

2. The finite element analysis method for stiffening rib plate unit according to claim 1, characterized in that: The calculation of the plane stress unit elastic modulus and the bending plate unit elastic modulus of the stiffening rib plate unit in the x-axis direction and the y-axis direction is performed, wherein: For the plane stress element elastic modulus of the stiffening rib plate element in the x-axis direction, specifically, in, represents the plane stress element elastic modulus of the stiffening rib plate element in the x-axis direction, represents the material elastic modulus of the stiffener plate element; For the elastic modulus of the bending plate element of the stiffening rib plate element in the x-axis direction, specifically, in, represents the elastic modulus of the bending plate element of the stiffening rib plate element in the x-axis direction; For the plane stress element elastic modulus of the stiffening rib plate element in the y-axis direction, specifically, in, represents the plane stress element elastic modulus of the stiffening rib plate element in the y-axis direction; For the elastic modulus of the stiffening plate element in the y-axis direction, specifically, in, Represents the elastic modulus of the stiffener plate element in the y-axis direction.

3. The finite element analysis method for stiffening rib plate unit according to claim 1, characterized in that: The plane stress unit elastic matrix and the bending plate unit elastic matrix are constructed, wherein: The plane stress unit elastic matrix is ​​specifically: in, represents the plane stress element elastic matrix, represents the plane stress element elastic modulus of the stiffening rib plate element in the x-axis direction, Indicates the intermediate quantity, , 、 Both represent intermediate quantities. , represents the material elastic modulus of the stiffener plate element, represents the plane stress element elastic modulus of the stiffening rib plate element in the y-axis direction, represents the Poisson's ratio of the stiffener plate element, , represents the material shear modulus of the stiffener plate element; The elastic matrix of the bending plate unit is specifically: in, represents the elastic matrix of the bending plate element, represents the elastic modulus of the stiffening plate element in the x-axis direction, Represents the elastic modulus of the stiffener plate element in the y-axis direction.

4. The finite element analysis method for stiffening rib plate unit according to claim 1, characterized in that: The plane stress unit stiffness matrix and the bending plate unit stiffness matrix are constructed, wherein: The plane stress unit stiffness matrix is ​​specifically: in, represents the plane stress element stiffness matrix, represents the strain matrix of the plane stress element, represents the matrix transpose, represents the plane stress element elastic matrix, The area domain representing the stiffener plate element surface; The bending plate element stiffness matrix is ​​specifically: in, represents the stiffness matrix of the bending plate element, represents the strain matrix of the bending plate element, represents the elastic matrix of the bent plate element.

5. The finite element analysis method for stiffening rib plate unit according to claim 1, characterized in that: The calculation of the internal forces and stresses of the plane stress unit and the bending plate unit is realized, wherein the calculation of the internal forces and stresses of the plane stress unit specifically includes: Calculate the stress of a plane stress element. Specifically, in, represents the stress of the plane stress element, represents the plane stress element elastic matrix, represents the element strain, , represents the strain matrix of the plane stress element, represents the unit displacement, , represents the matrix transpose, Represents the nodes in the stiffener plate element The displacement along the x-axis, Represents the nodes in the stiffener plate element Displacement along the y-axis; Calculate the internal forces per unit width of a plane stress element. Specifically, in, Represents the internal force per unit width of a plane stress element.

6. The finite element analysis method for stiffening rib plate unit according to claim 1, characterized in that: The calculation of the internal forces and stresses of the plane stress unit and the curved plate unit is realized, wherein the calculation of the internal forces and stresses of the curved plate unit specifically includes: Calculate the internal forces per unit width of the curved plate element. Specifically, in, represents the internal force per unit width of the bending plate element, represents the elastic matrix of the bending plate element, represents the strain matrix of the bending plate element, represents unit displacement, , represents the matrix transpose, Represents the nodes in the stiffener plate element The deflection along the z-axis is, Represents the nodes in the stiffener plate element The rotation angle around the x-axis, Represents the nodes in the stiffener plate element The rotation angle around the y-axis at ; Calculate the stress of the curved plate element. Specifically, in, represents the stress of the bending plate element, It represents the z-axis coordinate of the stress calculation point of the stiffening plate element in the direction of equivalent thickness in the x-axis direction, and the z-axis coordinate value of the top surface of the stiffening plate element in the direction of equivalent thickness in the x-axis direction is equal to , the z-axis coordinate value of the bottom surface of the stiffening rib plate element in the equivalent thickness direction of the x-axis direction is equal to , It represents the z-axis coordinate of the stiffening plate element in the equivalent thickness direction of the y-axis, and the z-axis coordinate value of the top surface of the stiffening plate element in the equivalent thickness direction of the y-axis is equal to The z-axis coordinate value of the bottom surface of the stiffening rib plate element in the equivalent thickness direction in the y-axis direction is equal to , The z-axis coordinate of the shear stress thickness direction of the stiffening plate element is equal to , the z-axis coordinate value of the shear stress thickness direction of the bottom surface of the stiffening rib plate element is equal to , Indicates the top plate thickness of the stiffener plate element.

7. A finite element analysis device for stiffening rib plate units, characterized in that: The stiffening rib plate unit finite element analysis device includes: Create a module for establishing the local coordinate system oxyz of the plate element based on the mid-surface of the stiffened plate element, where the oxy plane is located at the mid-surface of the plate, the z axis is perpendicular to the plate plane, the longitudinal stiffeners of the stiffened plate element are along the x-axis direction of the coordinate system, and the transverse stiffeners are along the y-axis direction of the coordinate system; a calculation module, which is used to respectively calculate the plane equivalent thickness and bending equivalent thickness of the stiffening rib plate unit in the x-axis direction, as well as the plane equivalent thickness and bending equivalent thickness in the y-axis direction, and calculate the plane stress unit elastic modulus and the bending plate unit elastic modulus of the stiffening rib plate unit in the x-axis direction and the y-axis direction based on the calculated plane equivalent thickness and bending equivalent thickness, so as to construct the plane stress unit elastic matrix and the bending plate unit elastic matrix; An execution module, which is used to construct a plane stress unit stiffness matrix and a bending plate unit stiffness matrix according to the plane stress unit elasticity matrix and the bending plate unit elasticity matrix, and realize the calculation of internal forces and stresses of the plane stress unit and the bending plate unit; The calculation of the equivalent thickness and bending equivalent thickness of the stiffening plate element in the x-axis direction, and the equivalent thickness and bending equivalent thickness in the y-axis direction, respectively, specifically includes: Calculate the equivalent thickness of the stiffener plate element in the x-axis direction. Specifically, in, represents the equivalent thickness of the stiffening plate element in the x-axis direction. represents the top plate thickness of the stiffener plate element, represents the area of ​​a single longitudinal stiffener in the stiffened plate element, Indicates the distance between two adjacent longitudinal stiffeners in the stiffener plate element; Obtain the position of the centroid of the equivalent section formed between the top plate of the stiffening rib plate unit and the longitudinal stiffener, and record the equivalent section as the first equivalent section, and then calculate the distance from the upper edge of the first equivalent section to the centroid of the first equivalent section , and the distance between the lower edge of the first equivalent section and the centroid of the first equivalent section ; Calculate the equivalent thickness of the stiffener plate element in the y-axis direction. Specifically, in, represents the equivalent thickness of the stiffening plate element in the y-axis direction. represents the area of ​​a single transverse stiffener in the stiffened plate element, Indicates the distance between two adjacent transverse stiffeners in the stiffener plate element; Obtain the position of the centroid of the equivalent section formed between the top plate of the stiffening rib plate unit and the transverse stiffener, and record the equivalent section as the second equivalent section, and then calculate the distance from the upper edge of the second equivalent section to the centroid of the second equivalent section , and the distance between the lower edge of the second equivalent cross section and the centroid of the second equivalent cross section ; Calculate the bending equivalent thickness of the stiffener plate element in the x-axis direction. Specifically, in, represents the bending equivalent thickness of the stiffening rib plate element in the x-axis direction, represents the transverse bending inertia moment of the top plate of the stiffened rib plate element relative to the centroid of the first equivalent section, Represents the transverse bending inertia moment of the longitudinal stiffener of the stiffened plate element relative to the centroid of the first equivalent section; Calculate the bending equivalent thickness of the stiffener plate element in the y-axis direction. Specifically, in, represents the bending equivalent thickness of the stiffener plate element in the y-axis direction, represents the transverse bending inertia moment of the top plate of the stiffened rib plate element relative to the centroid of the second equivalent section, Represents the transverse bending moment of inertia of the transverse stiffener of the stiffened plate element relative to the centroid of the second equivalent cross section.

8. A finite element analysis device for stiffening rib plate units, characterized in that: The stiffening rib plate unit finite element analysis device includes a processor, a memory, and a stiffening rib plate unit finite element analysis program stored on the memory and executable by the processor, wherein when the stiffening rib plate unit finite element analysis program is executed by the processor, the steps of the stiffening rib plate unit finite element analysis method according to any one of claims 1 to 6 are implemented.

9. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a stiffening rib plate unit finite element analysis program, wherein when the stiffening rib plate unit finite element analysis program is executed by a processor, the steps of the stiffening rib plate unit finite element analysis method according to any one of claims 1 to 6 are implemented.

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