热载荷作用下梯度多孔材料梁弯曲及过屈曲力学行为的研究

基于Bernoulli-Euler梁理论，引入物理中面解耦了复合材料结构的面内变形与横向弯曲特性，研究了梯度多孔材料矩形截面梁在热载荷作用下的弯曲及过屈曲力学行为．假设沿梁厚度方向材料的性质是连续变化的，利用能量法推导了矩形截面梁的控制微分方程和边界条件，并用打靶法对无量纲化的控制方程进行数值求解．利用计算得到的结果分析了材料的性质、热载荷、边界条件对矩形截面梁非线性力学行为的影响．结果表明，对称材料模型下，固支梁与简支梁均显示出了典型的分支屈曲行为特征，而其临界屈曲热载荷值均会随着孔隙率系数的增加而单调增加．非对称材料模型下，固支梁仍显示出分支屈曲行为特征，但其临界屈曲热载荷不再随着孔隙率系数的变化而单调变化；而对于两端简支梁，发生了弯曲变形，弯曲挠度随载荷的增大而增大．

Study on the Bending and Post-Buckling Mechanical Behaviors of Beam Made of Gradient Porous Material under Thermal Load

Based on the Bernoulli-Euler beam theory, the in-plane deformation and transverse bending characteristics of composite structures are decoupled by introduction of the neutral plane, and the bending and post-buckling mechanical behaviors of rectangular cross-section beams made of graded porous materials under thermal loads are investigated. Based on the assumption that the material properties change continuously along the thickness of the beam, the governing differential equations and the boundary conditions of the rectangular cross-section beam are derived by the energy method, and the dimensionless governing equation is solved numerically by the shooting method. The effects of material properties, thermal loads and boundary conditions on the nonlinear mechanical behavior of rectangular cross-section beam are investigated using the numerical analysis. The results show that for the symmetric material model, both the fixed beam and the simply supported beam exhibit typical branching buckling behavior, and their critical buckling thermal loads increase monotonically with the increase of porosity coefficient. For the asymmetric material model, the fixed beam still exhibits the branching buckling behavior. However, the critical buckling thermal load does not change monotonously with the porosity coefficient. For the beam with simple support at both ends, the bending deformation occurs, and the bending deflection increases with the increase of load.