JPH09243473A - System for analyzing contact stress - Google Patents

Abstract

PROBLEM TO BE SOLVED: To efficiently analyze a contact stress by dividing a structure to partial areas so that two confronting contact faces are in one partial area and data of each contact face required when a contact state of the contact face is to be corrected and calculated are on a memory device of one operational device. SOLUTION: In a process of analyzing a contact, if objects in contact with each other are allotted to different partial areas, i.e., different operational devices 6, it is necessary to transmit data between respective memory devices 7 of the operational devices 6 to estimate a contact state after a load is impressed. As such, the objects in contact with each other are allotted to the same memory device 7, thus eliminating the transmission of data between the memory devices 7. In a calculating process, at each initial stage of repetitions carried out until a surface force is balanced between the partial areas, the contact state analyzed immediately before is set as an initial value. Accordingly, the repeating number of times to calculate the contact is reduced.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a system for analyzing stress and deformation of a contact portion of a structure by using a parallel computer.

[0002]

2. Description of the Related Art There are roughly two methods for analyzing deformation and stress of a structure using a parallel computer. One of the methods is to represent the entire deformation characteristics as one simultaneous equation, and at the stage of solving the one simultaneous equation, distribute the components of the simultaneous equation to a plurality of arithmetic units and their associated storage devices, This is a method in which the device solves the distributed components. In this case, the variables in the system of equations are usually correlated with the variables assigned to other computing devices,
Each arithmetic unit performs calculation while referring to the calculation results of other arithmetic units. Another method is to divide the structure itself to be analyzed into a plurality of partial areas, distribute the information of each partial area to different arithmetic devices, and each arithmetic device analyzes the assigned partial area. Is. This method is usually called the area division method. In the contact analysis, it is necessary to satisfy the compatibility of the displacement of the contact surfaces facing each other at the contact portion and the force balance condition. Therefore, it is necessary to add the equations expressing these conditions of the contact part to the above simultaneous equations. Various addition methods have been devised. The representative ones are a method of directly adding the adaptive conditional expressions to the simultaneous equations, a method of indirectly adding the adaptive conditional expressions by a penalty function method, and the like. The present invention relates to speeding up when a structure having a contact portion is divided into a plurality of partial areas and analyzed by a plurality of arithmetic devices.

The reference document is "R. Glowinsk
i, QV Dinh, J. Periaux, DomainDecomposition Meth
ods for Nonlinear Problems in Fluid Dynamics, Comp
uterMethods in Applied Mechanics, Vol.40, pp.27 (1
983) '' `` G. Yagawa, Parallel Techniques for Computational
Mechanics, Theoretical and Applied Mechanics, Vo
l. 39, pp. 3 (1990) '' `` G. Yagawa, N. Soneda, S. Yoshimura, A Large Scal
e Finite ElementAnalysis Using Domain Decompositio
n Method on a Parallel Computer, Computers and
Structures, Vol. 38, No. 5/6, pp.615 (1991) "" Yoshioka, Yagawa, Yoshimura, Soneda, Development of network computing method for large-scale and ultrafast computational mechanics, The Japan Society of Mechanical Engineers Vol. (A), 57, 1964 (19
91) "" Okamoto, Analysis of Nonlinear Contact Problems by Finite Element Method, The Japan Society of Mechanical Engineers, Volume A, 43, 3716 (1977) "" Yagawa, Analysis of Two-Dimensional and Beam Contact Problems by Penalty Method , Transactions of the Japan Society of Mechanical Engineers (A), 46, 12
20 pages (1980) ".

[0004]

In the method in which the structure to be analyzed is divided into a plurality of partial areas and each partial area is analyzed by a different computing device, the boundary of each partial area is only the analysis result of each partial area. Since it is not determined from, the usual unknown variables at the boundary are set to appropriate initial values, and then each partial region is analyzed based on the initial values. Next, the validity of the set value at the boundary is verified from the analysis result of the adjacent partial areas. Normally, the forces are not balanced among the partial regions, so the initial value is corrected to a value that is expected to be balanced. This correction work is usually performed multiple times. In the contact analysis, the contact state of the contact portion, specifically, the contact range, the displacement of the contact portion, and the contact force are unknown before the load is applied, and the contact state after the load is predicted and calculated. If this prediction is not valid, correct it and analyze again. This correction iteration will also typically be multiple. Therefore, when the contact analysis is performed by the area division method, it is necessary to perform both the boundary part correction iteration of the partial area and the contact part correction iteration. It is necessary to transfer data between the arithmetic units during the correction iteration. In a parallel computer, the data transfer time between arithmetic units has a great influence on the calculation time. Therefore, how to reduce the data transfer is an issue related to the reduction of the total calculation time. An object of the present invention is to speed up the calculation when the contact structure is subjected to the area division method.

[0005]

In order to achieve the above object, the present invention divides a partial area of a structure so that two opposing contact surfaces become one partial area.
At this time, the data of each contact surface necessary for the calculation of the correction of the contact state of the contact surface is stored in the storage device of one arithmetic unit. In the convergence calculation of the boundary portion of the partial area of the structure, the result of the previous contact analysis is stored in each arithmetic unit, and the previous contact analysis result is used as the initial value of the contact state when recalculating the partial area. To use.

In this way, when the contact state of the contact surface is calculated for correction, the data of each contact surface is stored in the storage device of one arithmetic device, so that data transfer between arithmetic devices becomes unnecessary. Specifically, first, an initial value is given to the boundary portion of each partial area, and the deformation amount and the boundary reaction force are calculated in each partial area. In the calculation of each of the partial areas, the contact state set in the contact area is used as an initial value for iterative calculation. In this iterative calculation, it is not necessary to transfer the data from another arithmetic device because all the data required for the iteration are in the storage device of the arithmetic device. When the contact state converges, the analysis result of the boundary portion of each partial area is transferred to the storage device of the arithmetic unit that corrects the data of the boundary portion. The collected boundary analysis results are used to correct the boundary data so that the matching conditions of force and displacement are satisfied at the boundary, and the correction results are transferred to the storage device of the arithmetic unit in charge of each partial area. . Each arithmetic unit recalculates using the corrected boundary data. At this time,
As the initial value of the contact portion, the convergence calculation of the contact portion is accelerated by using the analysis result of the previous partial area.

[0007]

Embodiments of the present invention will be described below with reference to the drawings.

FIG. 1 shows an example of a structure to be analyzed. The structure 1 has a contact portion 2. In this example, there is one contact part, but the following description can be similarly applied to the case where there are a plurality of contact parts. In FIG. 2, the structure 1 is divided into a plurality of partial regions 3. The contact part 2 is one partial area 4
To be included in. Each partial area 3 or 4 is divided by a boundary portion 5. The calculation of the partial regions 3 or 4 is performed for each partial region by a different arithmetic device. FIG. 3 shows the state of the allocation, and the data of each partial area 3 or 4 is stored in the storage device 7 attached to a separate arithmetic device 6. The stored data is shape data of each partial area, material data, mechanical boundary condition data such as external force, displacement boundary condition data, and data indicating which boundary part 5 is connected to another partial area. is there. Since the displacement and the surface force at the boundary portion 5 are unknown at the initial stage of the analysis, an appropriate initial value is given for the calculation. The method of giving the initial value includes a method of giving a load on the boundary portion and a method of giving a displacement of the boundary portion. In the method of applying the load on the boundary part, there are few displacement constraints, which may result in the movement of the rigid body in the region. In that case, the displacement cannot be uniquely determined by the static analysis. Therefore, usually, the displacement is given as the initial value of the boundary portion. The closer to the correct answer the initial displacement is, the better, but it is difficult to predict it at the initial stage of analysis, so the displacement is usually set to zero. Using this initial value, the deformation and stress of each partial region are analyzed by different computing devices 6. In order for the obtained solution to be a correct solution, it is necessary that the two conditions of (1) the balance of the stress (surface force) and (2) the continuity of the displacement be satisfied on the region boundary of the adjacent partial regions. is there. That is, taking the case of two-dimensional analysis as an example, the condition on the boundary part 5 is

[0009]

[Equation 1]

[0010]

[Equation 2]

[0011]

(Equation 3)

[0012] The condition is required. In the above equation, the orthogonal coordinate axes are x and y, σ _x is the stress in the x-axis direction, σ _y is the stress in the y-axis direction, σ _xy is the shear stress in the y-axis direction applied to the plane perpendicular to the x-axis, and n _x is The x-axis direction component of the outward normal unit vector on the boundary portion 5, n _x is the y-axis direction component of the outward normal unit vector on the boundary portion 5, u _x is the x-axis direction component of the displacement, u _y represents the y-axis direction component of displacement, and the upper subscript represents a partial region. However, since both areas are in contact with each other on the boundary part 5,

[0013]

(Equation 4)

## EQU1 ##

The displacement and stress of the boundary portion 5 of each partial region analyzed by setting the initial value of the displacement in the boundary portion 5 satisfy the equation 3, but normally the equations 1 and 2 are satisfied. Absent. Therefore, after each partial region is analyzed by a different computing device, the assumed displacement of the boundary portion 5 is corrected to a direction that satisfies the equations 1 and 2. The simplest method of modification is called the Uzawa method, which is modified by the following formula.

[0016]

(Equation 5)

[0017]

(Equation 6)

Where ρ is a constant. Using the corrected displacement, the displacement and stress of each partial region are analyzed again.
The calculation of each partial region and the calculation of the boundary displacement correction are repeated until Expressions 1 and 2 are sufficiently satisfied. Specifically, the analysis result of each partial area is transferred from the storage device 7 through the data transfer path 10 to the storage device 9 attached to the arithmetic unit 8 which is in charge of the correction of the setting value of the boundary part, through the data of the boundary part. The arithmetic unit 8 corrects the boundary displacement based on the transferred boundary data of each partial area so that the mechanical equilibrium condition is satisfied at the boundary. This estimated correction data is transferred from the storage device 9 to the storage device 7 of each partial area. Each arithmetic unit 6 calculates the displacement and surface force of the partial area again using the corrected boundary data. The surface force of the boundary is calculated from the analysis result, and the data of the boundary is transferred to the storage device 9 again. This series of repetitive operations is performed until the surface force balance is satisfied between the partial areas.

In the contact analysis, the problem is how the contact state of the contact portion changes after loading. The contact state in the initial stage of analysis changes after loading, but the contact state itself is the boundary condition in the analysis, and the boundary condition changes in the loading process, which is a nonlinear analysis. Therefore, in the contact state before loading, first, the deformation of the contact surface and the surface force are obtained. Since the contact state after loading is different from the initial state, the opposing contact surfaces bite into each other, or the tensile force acts between the contact surfaces, resulting in a geometrically and mechanically incorrect state. Therefore, it is presumed that the part where the contact surface bites is in contact after the load and the part where the contact surfaces are pulled apart is separated after the load. In addition, we also estimate whether slippage will occur based on the relationship between frictional force and contact surface pressure. Analysis is performed again using this estimated value, and the deformation and surface force of the contact surface at that estimated value are obtained. As a result, when it is determined that the estimated contact state is not geometrically and mechanically correct, the contact state is estimated again and the analysis is re-executed. In this way, the analysis is repeated until a mechanically correct contact state is obtained.

In the contact analysis process, if the objects to be contacted are assigned to different partial areas, that is, to different computing devices 6, the storage device of each computing device 6 is used to estimate the contact state after loading. It becomes necessary to transfer data between the seven. In parallel computers, reducing data transfer contributes the most to calculation efficiency. Therefore, the contacting object is made to enter the same storage device 7, and the data transfer between the storage devices 7 becomes unnecessary.

In addition, in this calculation process, at each initial stage of the iteration performed until the balance of the surface forces is satisfied between the partial regions, the contact state is set as the initial value of the contact state of the analysis result immediately before. This can reduce the number of iterations of contact calculation and reduce the calculation amount.

[0022]

According to the present invention, data transfer and calculation amount can be reduced, and efficient analysis can be performed.

[Brief description of drawings]

FIG. 1 is an explanatory diagram of a structure to be analyzed.

FIG. 2 is an explanatory diagram of an example in which an analysis target is divided into a plurality of partial structures.

FIG. 3 is an explanatory diagram showing an arithmetic unit and a storage device of a parallel computer.

[Explanation of symbols]

1 ... Structure, 2 ... Contact part, 3 ... Partial structure, 4 ... Partial structure including a contact part, 5 ... Partial structure boundary part.

Claims (2)

[Claims] 1. A parallel computer having a plurality of arithmetic devices is used to divide a structure having a contact portion into a plurality of partial regions, and each partial region is calculated in parallel by a plurality of arithmetic devices to calculate the displacement of the structure. A contact stress analysis system characterized in that in a device for analyzing stress, opposing areas in contact are assigned to one computing device. 2. The predictive contact of a structural contact portion at the start of correction calculation, wherein an initial value is given to the boundary condition of the partial area, and the initial value is corrected based on the calculation result of each partial area. A contact stress analysis system that uses the contact state of the calculation result of each partial area before correction as the state.