基于CR列式的壳屈曲分析

Co-Rotational Formulation-Based Analysis of Shell Buckling

为解决薄壁结构屈曲分析的非线性计算问题,针对壳单元大位移、小应变分析,提出了基于更新拉格朗日CR列式的计算方法.该方法采用更新拉格朗日列式建立壳单元在大位移下的平衡方程,利用能量原理得到单元刚度矩阵.求解过程中,采用极分解方法计算变形后单元的随动坐标和单元节点的刚体转动;引入有限转动理论,从总位移中扣除刚体位移,得到节点变形,进而采用小应变理论计算单元应力,得到当前荷载步下的单元状态.最后,通过编制的程序对2个薄壳结构受力后的屈曲行为进行了分析.算例表明,用基于CR列式的非线性分析方法求解壳失稳问题具有较高的效率和精度.

In order to solve the nonlinear problem in analyzing the bulking of thin-walled structures,an updated Lagrangian co-rotational method for the nonlinear analysis of shell structures was presented.A program based on this method was developed,and 2 numerical examples of the buckling analysis of shell structures were given.In this method,an updated Lagrangian formulation is adopted to build the equilibrium equation of shell elements under large displacements,and then the tangent stiffness matrix is get with the energy theory.The polar decomposition theory is applied in the computations of the new co-rotational coordinates of elements and the rigid body rotations of nodes,and the finite rotation theory is introduced to separate rigid displacements from total displacements to get deformations of the nodes.As a result,stresses of an element can be calculated based on the deformations by using the small-strain theory to obtain the element state for the current load step.The numerical examples indicate that the nonlinear analysis method based on co-rotational（CR） formulation is efficient and accuracy in solving the buckling of shell structures.