JPH04204024A - Analyzing system for contact stress - Google Patents

Abstract

PURPOSE:To analyze the contact stress without re-inserting an element even when the contact face slides relatively large by sequentially switching an element which has zero rigidity and an element which has the rigidity not equal to zero, depending on the relative positional relationship of the contact face. CONSTITUTION:A contact element is a virtual five-node quadrangular pyramid so defined that the bottom faces 1, 2, 3, 4 are on one contact surface 8 and the apex 5 is at the confronting face 7. This element represents the contact condition between the foot of perpendicular 6 from the apex 5 to the bottom face and, the apex 5. What is of physical significance is when the foot of perpendicular 6 is within the bottom face. In the case where the five-node contact element is applied to (a), the rigidity of the elements 2, 11, 12, 3, 5 and 9, 1, 4, 10, 5 is set to be zero. When the apex 5 is moved because of the deformation as in the case (b), the elements 9, 1, 4, 10 are changed to be effective, and the rigidity of the elements 1, 2, 3, 4, 5 is turned to zero. Accordingly, even when a large relative movement occurs, it becomes possible to analyze the contact stress without re-dividing the element.

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Industrial Application] The present invention relates to a system and method for analyzing stress and deformation of contact parts of structures using an electronic computer.

[Conventional technology]

The method for analyzing stress and deformation at the contact surfaces of structures is
Typical methods are the finite element method and the boundary element method. These methods divide the object into partial regions called elements. In the finite element method, the interior of the object is divided into partial regions, and in the boundary element method, only the surface of the object is divided. In both techniques, the surface is divided into multiple regions.

The displacement and surface force of each partial region are approximated by interpolation using values at a plurality of representative points called nodes of the partial region. In contact analysis, the equations are solved by combining the relational expressions of displacement and surface force between nodes and partial regions of opposing contact surfaces. Various methods have been developed to create a simultaneous relationship between surface displacement and surface force. A typical example is a method of inserting virtual elements between contact surfaces. This virtual element is called a contact element, a joining element, etc., and has a rigidity equivalent to the continuity of displacement between contact surfaces, the equilibrium condition of surface force, etc.

, (Kanto original, Motoki Yayogi, Proceedings of the Japan Society of Mechanical Engineers (edition A)
Volume 51, No. 472 (December 1985), p. 2747)
[Problem to be Solved by the Invention] The stiffness of a contact element will depend on the contact state of the surface into which the element is inserted. That is, it is necessary to change the rigidity of the contact element depending on whether the surfaces are in contact or apart, and when in contact, whether it is stuck or sliding. Therefore, as the structure deforms under load, the stiffness of the contact element also changes. The problem here is when the relative slip is large. As can be seen from the definition of a contact element, some of its constituent nodes are on one face and the remaining nodes are on the other face. In this case, both surfaces to which the contact element belongs must be opposite. Therefore, in the conventional analysis method, if the relative slip is large, it is necessary to re-divide the contact elements.

This redivision needs to be performed according to the deformation and is complicated. Even in the case of slight) Jz deformation, the need for re-division immediately arises depending on the positional relationship of opposing nodes, resulting in restrictions on element division. The present invention aims to eliminate such restrictions on contact element division and the complexity of re-division.

[Means for Solving the Problems] In order to achieve the above object, in the present invention, the contact surface is divided into a plurality of finite regions, points are provided on the finite regions, and points on one finite region are connected to each other. A virtual element of a triangle, pentagonal pyramid, or quadrangular pyramid is inserted between the contact surfaces to express the relationship between surface force and displacement between it and the nearest divided finite region on the opposing contact surface, and Multiple virtual elements representing the relationship between surface force and displacement are inserted between a point on the area and the finite area that includes the previous point.

[Action] In the contact element configured as above, expresses the relationship between surface force and displacement between a point on the - side finite area and the nearest divided finite area on the opposing contact surface. The contact element has a rigidity corresponding to the contact state. That is, when the contact state at the apex of the contact element is fixed, the contact element is made to have a rigidity corresponding to the condition of continuous displacement and the equilibrium condition of the surface force at that position. If the sliding condition follows Coulomb's friction side, a continuous condition of displacement in the direction perpendicular to the contact surface, an equilibrium condition of surface force in the direction perpendicular to the contact surface, and rigidity corresponding to Coulomb's friction side are provided.

When in a separated state, it has a rigidity that corresponds to the condition where the surface force is zero. The stiffness of the contact element formed by a point on the finite area on the - side and an area other than the closest divided finite area on the contact surface facing it is assumed to be zero. When the leg of the perpendicular drawn from the apex of the contact element to the other surface comes outside the bottom surface of the contact element due to relative deformation of the contact surface, the stiffness of that element is assumed to be zero. At this time, among the other contact elements that have been inserted in advance and have zero rigidity, there are some that have the feet of the perpendicular drawn from the apex of the element to the bottom surface inside the bottom surface.

Therefore, the contact element is provided with rigidity corresponding to the contact state. In this way, by switching between elements with zero stiffness and non-zero stiffness one after another depending on the relative positional relationship of the contact surfaces, it is possible to analyze without reinserting the elements even when the contact surfaces undergo a large relative slip.

[Example 1 Embodiments of the invention will be described below with reference to the drawings.

FIG. 1 shows the contact elements used in the examples. This contact element is a virtual five-dimensional structure defined such that the base surfaces 1, 2, 3.4 are on one contact surface 8 (target surface) and the apex 5 is on the opposite surface 7 (contactor surface). It is a nodal pyramidal element. Since it is virtual, the volume of the contact element may be zero. This element runs from apex 5 to base 1,
It represents the contact condition between the foot 6 of the perpendicular line drawn in 2 and 3.4 and the vertex 5, and the physical meaning is that the foot 6 of the perpendicular line
This is the case when the planes are inside surfaces 1, 2, 3, and 4. Figure 2 shows
When the present invention is applied to this five-node contact element, in addition to contact elements 1, 2, 3, and 4.5, areas 9, 1, 4, 10, and 2 adjacent to areas 1, 2, and 3.4, ,11,12.13
With , as the base, contact elements sharing the vertex 5 are created multiple times. In the case of FIG. 2(a), contact elements 2, 11 .
l 2,3°5 and 9. The stiffness of the contact element 9, 1, 4.10 change to valid elements.The stiffness of contact elements 1, 2, 3, 4.5 changes to zero.In this way, the finite region of the contact surface that is not opposite to the node and the By inserting contact elements between them, even if a large relative movement occurs, analysis can be performed without re-dividing the elements.

FIG. 3 shows the number of vertices in FIG. 2 as 13. 14. ．． FIG. 3 is a horizontal view of an embodiment in which the number of holes is increased to four with a diameter of 15 degrees and 16 degrees. The contact elements here are 13 17 18°13 1
8 19.14 17 18.14 +819.14
19 20, 15 17 18°15 18. 19
,15 19 20.16 1819.16 19 2
It is on the + side of 0. Figures 3(b) and 3(c) show the effective contact elements when the apex position moves to the right.
).

In FIG. 3(b), the load at vertex 16 is zero, and in FIG. 3(c), the load at vertices 15 and 16 is zero.

FIG. 4 is a horizontal view of an embodiment in which the vertices of the contact elements are placed on both sides of the contact surface, and only the contact elements are inserted between the nodes of the contact surface and the opposing finite regions. . The contact elements here are 1317 18, '14 17
18,14 1819.15 18 19,15 1
9 20,1619 20.17 14 13,18
1413.18 15 14,19 15 14,19
There are 12 pieces: 16 15.20 16 15.

FIG. 4(b) and FIG. 4(C) show effective contact elements when the position of the vertex moves to the right. In FIG. 4(b), contact elements 171413.14 17 18
, 18 15 14. +518 19. 19 16
15. and the stiffness of 16192o changes to zero. When the relative movement parallel to the plane reaches the stage shown in FIG. 4(c), the effective contact element becomes zero. Figures 3(b) and 4(b)
), in the case of Fig. 3(b), node 20 and surface 1
Although the contact between 516 and 516 is not considered,
In the case of Figure (b), even though only the contact elements between the nodes of the contact surfaces and the opposing finite regions are inserted, the contact elements 201 represent the contact between the nodes 20 and the surfaces 15 and 16.
516 is enabled and contact between node 20 and surface 1516 is considered.

Figure 5 shows an example that can be applied to cases where the amount of relative movement is very large as shown in Figure 4 (c). This is a case in which both the insertion of the contact element shown in Figure 4 and the apexes of the contact element shown in Figure 4 are placed on both sides of the contact surface. In this case, in addition to the contact elements in FIG. 4, 13 18 19, 13 19 20
,1715 14.1? 16 15, 14 192
0.18 16 15,15 17 18.19141
Three elements have been added. FIGS. 5(b) to 5(d) show effective contact elements when the contact surfaces move relative to each other. In this way, if you insert a contact element between a node of the contact surface and a finite area in the vicinity that is not facing it, and place the vertices of the contact element on both sides of the contact surface, the amount of relative movement will be very large. It can be seen that even if there are many cases, the contact surface can be analyzed without subdividing the elements.

FIG. 6 shows a method of creating a hexahedral contact element with hexagonal nodes using the method of the present invention in which the vertices of the contact element are located on both sides of the contact surface. That is, from eight five-node contact elements to nodal contact elements 2122 23 24 25 2
Synthesize 6 27 28. The contact element produced in this way has the same properties as the application example shown in FIG. That is, as shown in FIG. 7, no matter which direction the relative movement of the contact surfaces parallel to the plane is, there is a valid contact element representing the contact of the contact surfaces.

In the above embodiment, the five-node square pyramid contact element shown in FIG. 1 was used, but the same operation can be performed using a four-node triangular pyramid contact element as shown in FIG. Furthermore, in the case of two-dimensional analysis, a three-node triangular contact element as shown in FIG. 9 may be considered, and the same application example as the five-node triangular pyramidal contact element can be considered.

[Effects of the Invention] According to the present invention, even when there is a large amount of relative movement parallel to the surface of the contact surface, the contact surface can be analyzed without re-dividing the elements.

[Brief explanation of the drawing]

1, 8 and 9 are explanatory diagrams of contact elements, and FIGS. 2 to 7 are explanatory diagrams showing embodiments of the present invention. 1.2,3,4.5... Node, 6... Leg of perpendicular line, 7
゜8...Object surface, 9, 10, 11, 12, 13, 1
4゜15.16,17,18,19,20,21,22
゜23. 24, 25, 26, 27, 28, 29, 30 ゜ 31. 32, 33, 34, 35, 36, 37, 38゜ l Figure No. , ? 1vI ('ξ9 -弗31i0(a) 3rdr'i:J(buil 4 口 (aan 5th figure busy) 5121(d) 62nd 712th) 8121st 98th

Claims (1)

[Scope of Claims] 1. An input section that inputs shape information, load information, and boundary condition information of a plurality of structures, and a calculation section that calculates deformation and stress of mutual contact parts of the structures from the information, In a contact stress analysis system consisting of an output unit that outputs calculation results, the contact surface is divided into multiple finite regions, points are set on the finite regions, and points on one finite region and the opposite contact surface are Insert a virtual triangular, regular pyramid, or quadrangular pyramid element between the contact surfaces that represents the relationship between surface force and displacement with the nearest divided finite region, and then A contact stress analysis system that is characterized by inserting multiple virtual elements that represent the relationship between surface force and displacement between finite regions that include points. 2. In claim 1, multiple virtual elements with zero rigidity are inserted between a point on one finite area and a neighboring finite area that is not facing it, and the elements are determined by the relative positional relationship of the contact surfaces. A contact stress analysis system that enables analysis without reinserting elements even when large relative slip occurs on the contact surface by switching the stiffness of the contact surface one after another. 3. A step of inputting shape information, load information, and boundary condition information of multiple structures, a calculation step of calculating deformation and stress of mutual contact parts of the structures from these information, and a step of outputting the calculation results. In the contact stress analysis method, the contact surface is divided into multiple finite regions, points are set on the finite regions, and points on one finite region and the nearest divided finite region on the contact surface opposite to it are Insert a virtual triangular, triangular pyramid, or quadrangular pyramidal element between the contact surfaces that represents the relationship between surface force and displacement between By inserting an element with zero stiffness and switching between elements with zero stiffness and non-zero stiffness one after another depending on the relative position of the contact surface, analysis can be performed without reinserting the element even when the contact surface has a large relative slip. A contact stress analysis method that makes it possible.