具有力边条件的层合圆柱薄壳的扭转屈曲

用一阶剪切变形理论的位移场推导出 5个屈曲平衡方程 .为解这 5个方程 ,采用 4个内力和一个法向位移为基本未知量 ,并设之为事先满足全部边条件的三角级数 .其余的内力、内力矩、位移和转角可通过算子矩阵求逆和本构关系由这些基本未知量来表达 .最后 ,采用 Galerkin法可得一以法向位移 w的 Fourier系数为未知量的特征值问题 ,由此可求出临界载荷和相应的屈曲波形

Buckling of Laminated Cylindrical Thin Shells under Torsional Load with Boundary Conditions Including Forces

The buckling of laminated cylindrical thin shells under torsional load with boundary conditions including forces was studied.The equations of buckled equilibrium were derived based on the displacement field of the first- order shear- deformation theory. To solve these equations,four stress resultants and one displacement were used as basic unknowns and assumed to have a Fourier series form which satisfies all boundary conditions.All other forces,moments,displacements and rotations can be expressed in terms of these basic unknowns by taking inverse of an operator and using the constitutive relations.Finally,the Galerkin procedure was used to obtain an eigenvalue problem with the Fourier coefficients of the normal displacement w as its variables. Solving the eigenvalue problem yields the critical load and the buckling mode.