Displacement solving method capable of improving stability and convergence of iterative method

Abstract

The invention discloses a displacement solving method capable of improving the stability and the convergence of the iterative method. The displacement solving method is characterized in that during finite element mesh division, singular unit models exist, and a non-diagonal dominant stiffness matrix is as a basis in a unit stiffness matrix; non-singular nodes in non-singular units and singular units are processed through the conventional iterative method; abnormal nodes in the singular units are improved in unit, such as the volume is used as a penalty function to perform pretreatment on the basis of a precondition conjugate gradient method. The method can correct non-diagonal dominant finite element equation sets, can reduce the frequency of iterations, is fast in convergence speed, and is stable in effect; the method firstly multiplies unit stiffness and displacement and then performs superposition, and this way, calculation of combined total stiffness which is large can be avoided; through a data structure of unit stiffness, the data is conveniently updated, and parallel computing is facilitated.

Description

technical field [0001] The invention relates to the technical field of structural mechanics, in particular to a displacement solution method based on improving the stability and convergence of an iterative method. Background technique [0002] Usually, when the finite element method is used for numerical analysis of collision impact problems, especially when simulating the structural response under high-speed impact loads, for example, in the process of projectile shooting and explosion, the situation of an entity before deformation and after tensile deformation is as follows: Figure 6 As shown in , the position of node A before the projectile shooting or explosion is as follows figure 1 , once the projectile hits the target or explodes, the entity deforms, and then the position and direction of point A change, becoming node A’ and line segment It is the displacement of node A during the deformation process, so how to find the displacement of this node? [0003] If you w...

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Problems solved by technology

[0010] With the development of finite element technology, more and more finite element problems have emerged. When using the above three methods to solve finite element problems, the number of iterations will be too large when solving displacements for very deformed grids. , the convergence speed is slow, does not converge, and some even have a large error between the obtained solution and the true solution, then the solver of the original method will fail

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