考虑横法向热应变的C~0型Reddy板理论和三角形板单元

考虑横法向热变形,建议了C0型Reddy理论,并用于分析复合材料层合/夹层板热膨胀问题。虽然考虑了横法向热应变,但不增加额外的位移变量。此理论位移场不含有横向位移一阶导数,构造有限元时仅需C0插值函数。基于这一模型,运用虚位移原理推导了复合材料板平衡方程以及构造了6节点三角形板单元,并分析了简支复合材料层合/夹层板的热膨胀问题。数值结果表明,建立的模型能准确分析复合材料层合/夹层板热膨胀问题,而忽略横法向热应变的理论分析热膨胀问题误差较大。

C0-type Reddy plate theory considering transverse normal thermal strain and triangular plate element

By considering transverse normal thermal deformation, this paper proposed a C⁰-type Reddy theory, which is used to analyze thermal expansion problems of laminated composite and sandwich plates.Although transverse normal thermal strain was taken into account, displacement variables are not increased.The first derivatives of transverse displacement have been removed from displacement field of the proposed model, so that the C⁰ interpolation functions are only required for the finite element implementation.Based on the proposed model, the equilibrium equations are obtained by using the principle of virtual displacements.Moreover, a six-node triangular element is constructed to analyze thermal expansion problems of simply-supported laminated composite and sandwich plates.Numerical results show that the proposed model can produce accurate response of laminated composite and sandwich plates under temperature loads, whereas the models neglecting transverse normal strain are less accurate.