基于本征方程求解复合材料梁几何非线性静力平衡

Geometric nonlinear static equilibria of composite beams using intrinsic formulation

对基于本征梁理论求解复合材料梁的几何非线性大变形屈曲问题进行了研究,根据材料属性利用渐近变分法确定复合材料梁的刚度矩阵,再根据本构方程和平衡方程求得其静力学行为,结果表明:对单层铺层的复合材料梁来说,刚度矩阵的耦合项可以忽略,其变形构型及梁末端的位移及转角的变化趋势与各项同性材料相同;对一个一般的复合材料梁来说,其刚度矩阵的耦合项不可忽略,耦合项对位移和转角的影响与施加在梁上的载荷大小有关,在载荷小于30 N,以耦合项50%的变化量为界,当变化量小于50%时,位移和转角的变化趋势与初始时相同,当变化量大于50%时,位移和转角的变化趋势发生很大的改变,但与解耦后的变化趋势相似。

Based on intrinsic beam theory, this paper solved the large deformation buckling problem of geometric nonlinear composite beams. Using the asymptotic variational method, we can get the stiffness matrix of the composite beam in light of material properties. Then, the static behavior of composite beams could be obtained through the balance equation and constitutive equation. The results show that if the composite beam has a single layer, the coupling terms of the stiffness matrix can be ignored and the trends of the deformation configuration, normalized displacements and rotations of the beam end are the same as the isotropic material beams. However, for a general composite beam, the coupling terms of its stiffness matrix cannot be ignored, and the impact of coupling term on displacement and rotation change regularly according to load. When the load is less than 10lb. if the amount of the coupling term change is less than 50%, the displacement and rotation are the same as the initial trends; however, if the change is greater than 50%, they will undergo great changes.