C~0型高阶锯齿理论及复合材料厚梁热应力分析

基于已有锯齿理论构造单元时,需使用满足单元间C1连续的插值函数,难于构造多节点高阶单元,而且精度较低。针对已有锯齿理论存在的问题,本文首先发展了C0型锯齿理论。通过虚位移原理推导出在热载荷作用下复合材料梁的平衡方程,并给出了简支复合材料层合梁解析解。基于发展的锯齿理论分析了复合材料夹层梁和层合梁热膨胀问题,并与其他理论结果对比。数值结果表明,发展的C0型锯齿理论能克服已有锯齿理论的难题。

Thermal stress analysis of thick composite beams based on C0-type higher-order zig-zag theory

The C¹ shape functions have to be required during previous zig-zag theory's finite element implementation,so it is difficult to construct higher-order elements based on the zig-zag theory.Moreover,it is less accurate in comparison with three-dimensional elasticity solutions.To overcome drawback of zig-zag theory,this paper proposes a C⁰-type zig-zag theory considering transverse normal strain.By using the principle of virtual displacements,the equilibrium equations of laminated composite beams subjected to thermal loads have been presented,and analytical results of composite beams with simply-supported boundaries are also given in this paper.By means of the proposed model,thermal expansion problems of laminated composite and sandwich beams have been analyzed,and the present results have been compared with the results obtained from other models.Numerical results show that the proposed model can overcome drawback of previous zig-zag theory.