受均布载荷的双模量陶瓷简支梁的有限元计算

Finite Element Calculation of Simply Supported Beam with Bimodulus Ceramic Subjected to Uniform Load

关键词:  应力球张量法  双模量  单模量  简支梁  有限元

Key words:  Stress balls tensor method  Bimodulus  Single modulus  Simply supported beam  Finite element

摘要:

为了验证应力球张量法是否适用于双向应力状态下的不同模量计算，以受均布横向载荷的拉压模量不等材料的简支梁为例，建立其有限元模型，利用所研发的模块对简支梁进行了结构分析。通过对比所得有限元解与其解析解的计算结果，确定了误差范围，分析了有限元解的变化规律及其合理性。结果表明:正应力的最大误差不超过4.5%，竖向位移的最大误差不超过5.4%，切应力的最大误差不超过3.5%，满足工程上的要求。应力球张量法适用于双向应力状态下不同模量计算。

Abstract:

In order to verify whether stress balls tensor method could be used to different moduli calculation under biaxial stress state or not，taking the simply supported beam of bimodulus materials subjected to uniformly transverse load as an example，the finite element model was established.The structural analysis of the beam was completed by using the developed module. By comparing the results of the finite element (FE) solutions and analytical solutions，the error range can be found. Variation and rationality of finite element method are analyzed. The results show that the maximum error of normal stress is not more than 4.5%，the vertical displacement error does not exceed 5.4% and shear stress is not more than 3.5%. It can fully meet the requirements of engineering. Stress balls tensor method can be applied for calculation of different moduli under biaxial stress state.