基于应力球张量法的不同模量陶瓷梁有限元分析

Finite Element Analysis of Ceramic Beam with Different Modulus Based on Stress Balls Tensor Method

关键词:  应力球张量；双模量；单模量；陶瓷梁  有限元解

Key words:  Stress balls tensor  Bimodulus  Single modulus  Ceramic beam  Finite element solutions

摘要:

针对具有拉压弹性模量不等特性的材料，由于其不能沿用经典弹性理论进行应力和变形分析，为解决其结构计算问题，提出通过判断应力球张量的正负来确定拉压弹性模量的新思想，并在ANSYS的基础上，开发了拉压模量不等材料的分析计算模块。以纯弯曲两端简支的陶瓷梁为例，建立其有限元模型，利用所开发模块对纯弯曲的陶瓷梁进行结构分析，通过对比所得的有限元解与其解析解的计算结果，确定误差范围，正应力的误差不超过2.1%，挠度的误差不超过3%，得出本文提出方法的可行性。通过对比按照单、双模量计算所得最大拉压应力有限元解之间的误差，发现随着拉压弹性模量比的减小，误差值随之增大，超过工程允许范围，得出不同模量理论应用于实际的重要性。

Abstract:

For the materials with different modulus of elasticity in tension and compression which can not follow the classical theory of elasticity for stress and deformation analysis，to solve the problem of the structure calculation，the idea by judging the sign of the stress balls tensor to determine the modulus of elasticity in tension or compression was proposed. Based on ANSYS，analysis and calculation modules of the materials with different modulus in tension and compression were developed. Taking the simply supported ceramic beam of pure bending as an example，the finite element model was established. The structural analysis of the ceramic beam was completed by using the developed module. By comparing the results of the finite element (FE) solutions and analytical solutions，the error range could be found. Error of stress was not more than 2.1% and the deflection error did not exceed 3%. Feasibility of the proposed method is proved. By comparing the errors of FE solutions of the maximum tensile(compressive) stress between bimodulus and the same modulus，it could be found that the error value increased as the ratio of elastic modulus in tension and compression reducing. Error exceeds the allowable range of engineering，so the application of different moduli theory is important.