Unconstrained static structural analysis method based on Householder transformation

Abstract

The invention discloses an unconstrained static structural analysis method based on Householder transformation. The unconstrained static structural analysis method includes the steps that step1, a structure rigid body displacement mode matrix X is built; step 2, six corresponding n*n order Householder matrixes Pi are built according to the rigid body displacement mode matrix X; step 3, the Householder matrixes Pi built in the step2 are used for performing orthogonal similar transformation on a structure original rigidity matrix to obtain a structure rigidity matrix Kp with a rigid body mode removed; step 4, a correction conjugate gradient method is adopted for solving the rigidity equation (KPUP=FP) which is obtained after removing the structure overall rigid body displacement mode by the Householder matrixes. The structure rigid body displacement mode is removed, and the appointed minimum error threshold value of the conjugate gradient method is controlled, so that structural response is accurately solved; calculation and implement steps are concise, and it is unnecessary to modify a finite element calculation frame commonly used currently; by the adoption of the correction conjugate gradient method, the sparse characteristic of the structure rigidity matrix can be used well, and due to step solution, the overall solving process is small in occupied space and high in calculation efficiency.

Description

technical field [0001] The invention relates to structural analysis of finite elements, in particular to a finite element analysis method for structural mechanics problems in an unconstrained state. Background technique [0002] Usually, when performing linear static analysis, it is necessary to ensure that the structure has no rigid body displacement, otherwise the solver cannot calculate it. However, many problems in space do not have enough constraints. For example, when an airplane is flying, a ship is sailing, or goods are hoisted on a crane, in order to calculate the stress distribution on the structure, a special unconstrained structural static analysis method is required. . Existing analysis methods fall into the following categories. [0003] 1) Inertia release method, the basic idea is to use the inertial (mass) force of the structure to balance the external force. Although the structure is unconstrained, the analysis assumes it is in a "static" equilibrium. Wh...

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Problems solved by technology

[0005] With the popularization of finite element technology, various unconstrained problems emerge. When solving them with traditional finite element method, we will encounter the problem of singularity of stiffness matrix.

However, the existing unconstrained problem solving methods such as the inertia release method need to introduce the concept of virtual support. Since the virtual support is not a real displacement constraint, it will produce a large error compared with the real situation, and it needs to solve the equation, and the efficiency is sometimes Low; dynamic relaxation method is efficient but low precision due to explicit analysis method

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