各向同性轴对称复合圆板的三维线性分析

复合板具有优异的结构性、良好的性重比及其性能可设计性,在船舶工业中获得了广泛应用.为考察复合板的力学行为,对在均匀横向载荷下的各向同性轴对称复合圆板采用位移解法,根据结构变形的可能规律,设定位移解函数形式,将变量分离,进行了三维线性分析,构造了弹性力学计算模型,给出了一般板、层合板、夹芯板满足三维线性平衡方程、中面固支边界条件、层间连续条件的精确解.该解考虑了中面应变的影响,不同于Timoshenko-Goodier理论解.通过计算表明单层板、层合板解在一定的径厚比内,与Ansys计算结果十分接近,为固支圆板在均布横向载荷下的精确解.夹芯板实验证实,夹芯板理论解可更精确地预测面板中的应力、应变分布.

Linear three-dimension analysis of sandwich axially symmetrical circular plates

Due to its efficient performance and application to the ship industry, the 3-D mechanical study is being noticed. After constructing some elasticity models, a set of close three-dimensional linear analytical solutions, taking into account of all the normal stresses, shear stresses and satisfying all the equations of equilibrium, the mid-plane clamped boundary conditions and interfacial continuity conditions through-thickness, are presented for axially symmetrical homogeneous isotropic circular plates, laminates and sandwich plates under uniform transverse load by using the variable-separating method and formulating a set of displacement functions. The solutions are different from Timoshenko-Goodier's, taking into account of the effect of mid-plane strains. Some examples show that the solutions for homogeneous isotropic circular plates and laminates are agreement with Ansys in a scope of thickness/radii. The experimental results show the solution for sandwich is more accurate than others.