两端固支叠层圆柱厚壳轴对称问题的精确解析解

Based on the three-dimensional basic equations of elasticity in cylindrical coordinates , the statespace method was used to solve axisymmetric problem of thick single and laminated cylindrical shells withtwo clamped ends.To satisfy strictly the boundary conditions of the clamped ends , boundary displacementfunctions introduced into the state equations as state variables , the nonhomogeneous state equations weretransformed into the homogeneous state equations by employing the dimensional expanding method , andvariable coefficient state matrixes were changed into constant coefficient matrixes with the approximatelaminate technique by dividing the layer into sub-layers.The three-dimensional basic equations of elasticityand all the boundary conditions are satisfied strictly , the exact three-dimensional analytical solutions are obtained.The results of two examples show that the present solutions obtained have high precision by com-paring with FEM (Finite Element Method) solutions , and have good constringency with the number of se-ries terms and sub-layers. In addition , the influences of thickness-radius ratio and span-radius ratio on thedistributions of the displacements and stresses of cylindrical thick shells along the radial and axial direc-tions are analyzed.