Based on the kinetic equations of the gear mesh impact, SPH discrete equations were established. Numerical simulation was carried out on the meshing impact process of the gear, and stress and strain of each discrete point were obtained. After data processing, stress propagation was calculated, which shows stress distribution on tooth-profile surface. It is concluded that the stress concentrate mainly occurs in the pitch circle. The paper provides an effective new numerical simulation algorithm to gear mechanical properties analysis.
In this paper, based on the basic principle of the SPH method’s kernel approximation, a new kernel approximation was constructed to compute first-order derivative through Taylor series expansion. Derivative in Newton’s method was replaced to propose a new SPH iterative method for solving nonlinear equations. The advantage of this method is that it does not require any evaluation of derivatives, which overcame the shortcoming of Newton’s method. Quadratic convergence of new method was proved and a variety of numerical examples were given to illustrate that the method has the same computational efficiency as Newton’s method.
This article presents the gear modeling method in dynamic mechanical analysis using
SPH (Smoothed Particle Hydrodynamics) analysis method. The parameter equations of the
transition curve of gear root and the other parts of gear are decided. The 3D discrete particles model
is established based on the parameter equations. The SPH pre-process program of global and local
dividing is developed. The error between the divided discrete particles and theoretical profiles of
the gear has been analyzed. The analysis results show that this modeling method is a relatively
better method and the correct SPH discrete particles can be divided by this method.
Bone is a dynamic living tissue that undergoes continuous adaptation of its mass and structure in response to mechanical and biological environment demands. In this paper, we firstly propose a mathematical model based on cross-type reaction diffusion equations of bone adaptation during a remodeling cycle due to mechanical stimulus. The model captures qualitatively very well the bone adaptation and cell interactions during the bone remodeling. Secondly assuming the bone structure to be a self-optimizing biological material which maximizes its own structural stiffness, bone remodeling model coupled with finite element method by using the add and remove element a new topology optimization of continuum structure is presented. Two Numerical examples demonstrate that the proposed approach greatly improves numerical efficiency, compared with the others well known methods for structural topology optimization in open literatures.
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