考虑横法向热应变的C^0型Reddy层合梁理论

C^0-type Reddy's beam theory considering transverse normal thermal strain

考虑横法向热变形和自由表面条件,发展了C0型Reddy层合梁理论。考虑了横法向热应变,发展的C0型Reddy层合梁理论没有增加额外位移变量。发展模型的位移场不含有横向位移一阶导数,方便构造多节点高阶单元。基于虚位移原理,推导出复合材料层合梁的平衡方程并分析简支复合材料层合/夹层梁热膨胀问题。数值结果表明,建立的模型能准确分析复合材料层合/夹层梁热膨胀问题。然而,忽略横法向热应变的理论误差较大。

By considering the transverse normal thermal deformation and the free surface conditions, a C0- type Reddy＇s theory for laminated composite beams is proposed. Although transverse normal strain is taken into account, the number of the unknown offset variables in the proposed model is not increased. Moreover, the first derivatives of transverse displacement are taken out from the in-plane displacement fields, so that it is convenient to construct higher-order elements. Based on the principle of virtual displacement, the equations of equilibrium for laminated composite beams are presented, and the thermal expansion problems of laminated composite and sandwich beams are studied. Numerical results show that C0-type Reddy＇s beam theory considering transverse normal thermal strain can accurately analyze the thermal expansion problems of laminated composite structures. However, the models neglecting transverse normal strain are less accurate.