Mehdi Bohlooly

The paper presents an investigation to find a method for assessing the intensity of extension-bending mechanical coupling in the behavior of thin plates. The analysis considers thin, simply supported square laminate plates subjected to in-plane compression. Plates with various plies stacking sequences with extension-bending coupling phenomenon were analyzed employing the finite element method software and using a developed closed-formed equation – the analytical method. The coupling intensity was quantified using two dimensionless stiffness reduction coefficients and a nondimensional anisotropic coefficient, known from literature. A reduction in the buckling load for plates with different layer arrangements, observed during nonlinear analysis, was used as a measure of coupling intensity. The results revealed that laminates with high extension-bending coupling intensity could exhibit up to 19% reduction in the buckling load. Additionally, the individual contributions of coupling intensity parameters to this reduction were identified. The validity of the proposed method was further evaluated for plates with different boundary conditions. These findings provide a foundation for predicting the behavior of mechanically coupled laminates without the need for extensive stability analysis.

This study presents a novel approach for optimizing the critical buckling load of the stiffened piezolaminated composite plates using a self-adaptive special relativity search (SASRS) algorithm. The fiber orientations in the layers are considered as design variables. The stability equations are first derived based on the classical laminated plate theory (CLPT) with von Karman nonlinearity. The optimization problem is implemented in MATLAB. The optimization results are obtained to indicate the effecs of various boundary conditions, applied voltages, grid shapes, angles of diagonal ribs, and plate aspect ratios on the optimal design. Numerical investigations are carried out for 10-ply symmetrical stiffened piezolaminated plates. The robustness and efficiency of the proposed SASRS algorithm in maximizing the critical buckling load of the stiffened piezolaminated plates are demonstrated by comparing the optimized results from the standard special relativity search (SRS) algorithm. It is found that the proposed optimization method has better performance than the SRS algorithm.

It is widely recognized that certain structures, when subjected to static compression, may exhibit a bifurcation point, leading to the potential occurrence of a secondary equilibrium path. Also, there is a tendency of deflection increment without a bifurcation point to occur for imperfect structures. In this paper, some relatively unknown phenomena are investigated. First, it is demonstrated that in some conditions, the linear buckling mode shape may differ from the result of geometrically nonlinear analysis. Second, a mode jumping phenomenon is described as a transition from a secondary equilibrium path to an obscure one as a tertiary equilibrium path or a second bifurcation point. In this regard, some non-square plates with unsymmetric layer arrangements (in the presence of extension–bending coupling) are subjected to a uniaxial in-plane compression. By considering the geometrically linear and nonlinear problems, the bucking modes and post-buckling behaviors, e.g., the out-of-plane displacement of the plate versus the load, are obtained by ANSYS 2023 R1 software. Through a parametric analysis, the possibility of these phenomena is investigated in detail.

The paper deals with bifurcation and/or non-bifurcation post-buckling curves of composite plates under biaxial compression. For different lay-up sequences, a coupling, i.e. extension-bending (EB) is considered. The current investigations present distinct equilibrium paths describing when they have bifurcation-type and/or non-bifurcation-type responses. The novel parameter (i.e. EB coupling imperfection) is calculated to show the amount of non-bifurcation in the equilibrium path as a quantitative parameter. For the case of non-square plates, a novel mixed-mode analysis is conducted. The effects of different characters in laminated composites such as layer arrangement, loading ratio, aspect ratio, and boundary conditions are investigated. A novel result concluded in the numerical examples where there are some possibilities to have different mode shapes in linear and non-linear buckling analysis. FEM results of ANSYS software verify the results of analytical equations.