Abstract

The purpose of this study is to investigate the buckling characteristics of a sandwich beam consisting of a porous ceramic core (Alumina), two bottom and upper layers which are gradually changed from ceramic (Alumina) to metal (Aluminum) through the thickness direction. A core with three kinds of porosity patterns is considered. Shear deformation effects are taken into account based on third-order shear deformation theory (TSDT) and a two-variable refined shear deformation theory. Based on the physical neutral axis of the beam, the governing equilibrium equations for buckling are obtained using the principle of virtual work and are solved for different end conditions using the differential transform method (DTM). A parametric study on buckling behavior is conducted to focus on the influences of length-to-thickness ratio, volume fraction of FGM in two FG layers, and three porosity patterns, namely, uniform, asymmetric and symmetric distribution of porosity in a ceramic core for clamped-clamped, pinned-pinned and cantilever beams. The convergence and comparison studies are carried out. It is demonstrated that the critical buckling load for an FG three-layer-beam, with an asymmetric pattern in a porous ceramic core, is higher than the two other ones. In addition, as demonstrated, DTM is an efficient and reliable method to be employed in this area of solid mechanics.

摘要

本研究的目的是研究由多孔陶瓷芯（氧化铝）、两个底层和上层组成的夹层梁的屈曲特性，这些层在厚度方向上逐渐从陶瓷（氧化铝）变为金属（铝）。考虑具有三种孔隙率模式的岩心。基于三阶剪切变形理论 (TSDT) 和双变量精细剪切变形理论，考虑了剪切变形效应。基于梁的物理中性轴，利用虚功原理获得屈曲的控制平衡方程，并使用微分变换方法（DTM）求解不同的末端条件。对屈曲行为进行了参数化研究，重点关注长厚比的影响，FGM 在两个 FG 层中的体积分数，以及三种孔隙率模式，即陶瓷芯中孔隙率的均匀分布、不对称分布和对称分布，用于夹紧夹紧、固定固定和悬臂梁。进行收敛和比较研究。结果表明，在多孔陶瓷芯中具有不对称图案的 FG 三层梁的临界屈曲载荷高于其他两个梁。此外，正如所证明的，DTM 是一种有效且可靠的方法，可用于该固体力学领域。结果表明，在多孔陶瓷芯中具有不对称图案的 FG 三层梁的临界屈曲载荷高于其他两个梁。此外，正如所证明的，DTM 是一种有效且可靠的方法，可用于该固体力学领域。结果表明，在多孔陶瓷芯中具有不对称图案的 FG 三层梁的临界屈曲载荷高于其他两个梁。此外，正如所证明的，DTM 是一种有效且可靠的方法，可用于该固体力学领域。