热和机械载荷共同作用下Timoshenko夹层梁的非线性分析

Nonlinear Analysis of Timoshenko Sandwich Beams under Thermal and Mechanical Loads

在精确考虑轴线伸长和基于一阶横向剪切变形理论的基础上建立Timoshenko夹层梁在热载荷和机械载荷共同作用下的几何非线性控制方程,采用打靶法数值求解所得强非线性2点边值问题,获得了两端不可移简支和两端固定夹层梁在横向非均匀升温和横向均布压力作用下的静态非线性弯曲和过屈曲变形数值解.绘出了梁的变形随载荷参数、材料厚度和长细比等参数变化的特性关系曲线,并分析和讨论了这些参数对平衡路径的影响.

On the basis of accurately considering axial extension and the first-order transverse shearing, geometrically nonlinear governing equations for sandwich Timoshenko beams subjected to both thermal and mechanical loads are formulated. By using a shooting method the strongly nonlinear ordinary differential equations with two-point boundary conditions are solved and numerical solutions for static post-buckling and nonlinear bending of the sandwich Timoshenko beams, with pinned-pinned and fixed-fixed ends, subjected to both transversely non-uniform temperature rise and transverse distributed loads, are obtained. Characteristic curves of the nonlinear deformation of the beam changing with parameters of the loads, the material properties, the laminated thickness and the slenderness are plotted. Effects of all these parameters on the equilibrium paths of the beam are discussed.