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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。
In order to solve the problem of structural calculation, it is proposed to determine the tensile modulus of elasticity by judging the positive and negative of stress tensor tensor, because the material can not follow the classical elasticity theory. Based on the new idea of ANSYS, an analysis and calculation module with different tensile and compression modulus was developed. A simple finite element model of a purely curved ceramic beam with purely curved ends was established. The structure of the purely curved ceramic beam was analyzed by using the developed module. By comparing the calculated results with the analytical solutions, the error range, The error of normal stress is no more than 2.1% and the error of deflection is no more than 3%. The feasibility of the proposed method is obtained. By comparing the errors between the finite element solutions of the maximum tensile and compressive stresses calculated according to the single and the dual modulus, it is found that as the elastic modulus ratio of the tension and compression decreases, the error value increases and exceeds the allowable range of the project, Modular theory applies to practical importance.