Abstract

Present investigation deals with the snap-through phenomenon in a thermally pre-buckled or post-buckled reinforced composites beam. Composite laminated beam is reinforced with graphene platelets (GPLs) where the weight fraction of GPLs may vary in each layer. The governing equations of the beam are obtained by means of the first order shear deformation beam theory and the von-Kármán type of kinematic assumptions. The conventional Ritz method with Chebyshev polynomials is used to discretize the governing equations and establish a set of non-linear equations dealing with the response of a beam under the action of thermal and mechanical loads. Furthermore, the case of uniform temperature elevation in the beam and uniform lateral pressure is considered. At first, the response of the beam under uniform temperature elevation is obtained. Depending on the magnitude of temperature rise, beam may remain flat or undergo thermal post-buckling. Using the displacement control strategy, the non-linear eigenvalue problem is solved. After that the response of the pre-buckled or post-buckled beam subjected to uniform lateral pressure in large deflection is evaluated. Due to the possibility of snap-through phenomenon, the cylindrical arch-length technique is employed. At first, two comparison studies are provided to assure the validity and efficiency of the developed formulation. After that, novel numerical results are given to discuss the effects of temperature change, weight fraction of GPLs, distribution pattern of GPLs and boundary conditions. It is shown that the limit loads of the snapping phenomenon and the intensity of the snap-through phenomenon are highly dependent to the mentioned factors.

摘要

目前的研究涉及热预屈曲或热屈曲后增强复合材料梁中的弹跳现象。复合层压梁用石墨烯薄片 (GPL) 加固，其中 GPL 的重量分数在每一层中可能不同。梁的控制方程是通过一阶剪切变形梁理论和von-Kármán 类型的运动学假设获得的。采用切比雪夫多项式的传统 Ritz 方法对控制方程进行离散化，并建立一组处理梁在热载荷和机械载荷作用下的响应的非线性方程。此外，还考虑了梁中均匀升温和均匀侧压的情况。首先，获得梁在均匀升温下的响应。根据温度升高的幅度，梁可能保持平坦或经历热后屈曲。使用位移控制策略，解决了非线性特征值问题。之后，评估预屈曲或后屈曲梁在大挠度下受到均匀侧压力的响应。由于可能出现折断现象，因此采用了圆柱形拱长技术。首先，提供了两项比较研究，以确保所开发配方的有效性和效率。之后，给出了新颖的数值结果来讨论温度变化、GPL 的重量分数、GPL 的分布模式和边界条件的影响。