非均匀升温下Timoshenko夹层梁热过屈曲精确数学模型及其数值解

在精确考虑轴线伸长和一阶横向剪切变形的基础上建立Timoshenko夹层梁在热载荷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边值问题,获得两端不可移简支夹层梁在横向非均匀升温作用下的静态热过屈曲和热弯曲变形数值解.绘出梁的变形随温度载荷变化的特征关系曲线,分析和讨论材料和几何参数对梁变形的影响.结果表明:梁在均匀加热下不产生拉-弯耦合变形及弯曲变形.在均匀升温条件下,梁的中点无量纲挠度与升温的关系曲线为热过屈曲平衡路径;当升温为横向非均匀的情况下,中心挠度与平均升温之间的关系曲线表现出热弯曲变形的特点.横向剪切变形随梁的长细比增大而显著减小,随变形程度的增大而增大.

Exact mathematical model and its numerical solution of sandwich Timoshenko beams subjected to non-uniform temperature rise

On the basis of accurately considering the axial extension and first-order transverse shearing,geometrically nonlinear governing equations for sandwich Timoshenko beams subjected to thermal load were formulated.By using a shooting method,the strongly nonlinear ordinary differential equations with two-point boundary conditions were solved and numerical solutions for thermal post-buckling and bending deformation of sandwich Timoshenko beam with pinned-pinned ends and subjected to transversely non-uniform temperature rising were obtained.Characteristic curves of the nonlinear deformation changing with the thermal load were plotted.Effects of the geometric and material parameters on the deformation of the beam were discussed and analyzed in detail. The theoretical analysis and numerical results showed that there were no bending and stretching-bending coupled deformations in the beam under the transversely uniform temperature rise.Curves of the dimensionless midpoint deflection of the beam versus the temperature rise were thermal post-bucking equilibrium paths under uniform temperature rise.However,those curves were characteristic ones for the thermal bending under transverse non-uniform temperature rise.The transverse shearing deformation decreased obviously with the increase of the slenderness ratio and increased with the increase of total beam deformation.