应用数学和力学2025，Vol.46Issue(7)：867-881,15.DOI:10.21656/1000-0887.450139
一般边界条件下层合圆柱壳轴对称弯曲的精确解
Exact Solutions for Axisymmetric Bending of Laminated Cylindrical Shells With General Boundary Conditions
摘要
Abstract
Due to the excellent properties of materials and structures,composite laminated cylindrical shells are widely used in such key fields as chemical,marine and aerospace engineering.However,the local mechani-cal responses near the interfaces and boundaries are complex and affect the performances of the structures.As an effective method to obtain the exact solutions of the laminated structures,the state space method needs the numerical simulation to deal with the non-simply supported boundaries.Based on the state space framework for laminated cylindrical shells,the boundary displacement functions at the non-simply supported ends were intro-duced into the state equations as state variables,and homogeneous state equations were established to strictly satisfy the boundary conditions.Then,the variable coefficients in the state equations were converted to con-stants with the lamination approximate method,and the transfer relations of the mechanical quantities along the thickness of the laminated cylindrical shell were established.Finally,the loading conditions on the surfaces of the cylindrical shells were introduced with the Fourier series,and the exact solutions to the axisymmetric ben-ding problems were obtained.The examples show that,the present solutions are consistent with the finite ele-ment ones,and give the exact distributions of the stresses and displacements along the axial and radial direc-tions of the laminated cylindrical shells.In addition,the displacement and stress distributions near the clamped and free ends help illustrate the end effects of the two constraints.关键词
一般边界条件/轴对称弯曲/状态空间法/边界位移函数/层合圆柱壳Key words
general boundary condition/axisymmetric bending/state space method/boundary displacement function/laminated cylindrical shell分类
数理科学引用本文复制引用
胡文锋,冯金胜,孟侨,师雷,朱军,曹正文..一般边界条件下层合圆柱壳轴对称弯曲的精确解[J].应用数学和力学,2025,46(7):867-881,15.基金项目
国家自然科学基金(12102001) （12102001）
