Hexahedron element finite mass point method

Abstract

A hexahedron element finite mass point method comprises the following steps that firstly, model parameters are initialized, mass point displacement is updated, then, mass point pure deformation is solved through inverse motion of a hexahedron element, then mass point internal force is calculated, and finally, the mass point internal force is substituted into a central difference motion formula to solve the next mass point displacement. The steps of reverse rotation of a hexahedron unit and establishment of a local coordinate system of a traditional finite mass point method are improved, displacement and internal force of the mass point are updated through iterative calculation, the calculation accuracy is further improved, the calculation efficiency is improved on the premise that the calculation precision is guaranteed, the rigid body rotation high-order error is effectively reduced, the calculation process is simplified, and the derivation process is simpler and clearer. The derivation process and method are also suitable for other types of entity units, and have universal application significance.

Description

technical field [0001] The invention belongs to the field of structural mechanics, and in particular relates to a hexahedron unit finite particle method. Background technique [0002] The finite particle method is a structural analysis-oriented numerical analysis method based on particle motion and vector structural mechanics. It can also accurately analyze structural discontinuities and nonlinear problems; this method no longer uses the concept of continuum as an analysis object , but based on Newton's law of motion, the real physical model is discretized into a particle system with a finite number of particles, and the independent motion between the particles is analyzed; the structural motion deformation time is decomposed into a finite number of time periods, and each time period is a Path unit, the length of the path unit is the iterative step size, in each path unit, the force and motion of each particle is calculated, the position of the particle is iteratively calcul...

AI Technical Summary

Problems solved by technology

However, the current research on the finite particle method is still in the preliminary stage. There are many studies on rod, beam, plane membrane and thin shell elements, and less research on solid elements, especially hexahedron elements.

The reverse motion step in the current traditional hexahedral element finite particle method uses the hexahedral element particle as the origin of the local coordinate system to solve the pure deformation of the particle. Although most of the rigid body displacement of the element is also eliminated, the residual error is only a high-order error compared to the pure deformation of the particle. , but the pure deformation of some particles of the element is artificially returned to 0, which leads to uneven distribution of high-order errors and increases the calculation error. Although the traditional hexahedral element finite particle method solves the particle with a pure deformation of 0 nodes through the moment balance relationship of the element internal force, but it increases the fluctuation of the internal force value of the particle during the iterative calculation of the unit, and requires a smaller iteration step size to prevent the divergence of the central differential motion formula, which increases the number of iterations and reduces the calculation efficiency

And the current traditional hexahedral element finite particle method judges the positive and negative of the rotation angle and vector modulus many times in the in-plane rotation step, which makes the calculation process more complicated

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