基于神经网络的弹性力学位移计算方法研究

Research on Neural Network-Based Computational Methods for Elasticity Displacement in Mechanics

常规的弹性力学问题是以有限元方法为主进行数值求解的,网格划分对计算结果影响较大,从而在求解力学问题时存在一定的局限性。神经网络作为一种通用数值逼近器,可以用来实现对弹性力学偏微分方程的求解。本文建立了基于物理约束的神经网络偏微分方程求解模型,以常见的二维平面压缩计算为例,实现了该方法的求解和验证,为智能化弹性力学求解提供了新思路与方法。

Conventional elasticity problems are primarily numerically solved using finite element methods,where mesh partitioning significantly influences computational results,leading to certain limitations in solving mechanical problems.Neural networks,as a versatile numerical approximator,can be employed to solve partial differential equations in elasticity mechanics.This paper establishes a neural network partial differential equation solving model based on physical constraints.Taking the example of common two-dimensional plane compression calculations,the method's solution and validation are implemented,providing new ideas and methods for intelligent elasticity problem-solving.