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This paper investigates the instability and buckling characteristics of a porous microplate under the influence of electrostatic fields, taking into account the implications of the intermolecular Casimir forces. Employing the modified couple stress theory, this research formulates equations that encapsulate the interplay between electrostatic and Casimir forces within porous plates. The analysis integrates distributed support loads, employing both Galerkin mode summation and finite element methods to solve static deformation equations and determine pull-in instability voltages and buckling loads. A novel approach is introduced, and equilibrium relationships are derived with respect to displacement to determine both the buckling load and instability voltage. This study effectively compares classical and non-classical theories, scrutinizing the effects of dimensionless length scale parameters and porosity ratios on maximum displacement, pull-in instability voltages, and buckling loads. The results demonstrate that the analytical method converges swiftly and aligns with the findings of the finite element method. The method for deriving equilibrium relationships proves to be accurate in predicting both instability voltage and buckling load. Additionally, the instability voltage exhibits an almost linear relationship with variations in the percentage of porosity, and similarly, the buckling load undergoes linear changes with alterations in porosity percentage. Hence, formulas for the linear relationships are calculated for both of these associations. [ABSTRACT FROM AUTHOR]

The stability behaviour of unsymmetrical laminated structures made of fibre-reinforced plastics is significantly influenced by bending–extension coupling and the comparatively low transverse shear stiffnesses. The aim of this work is to improve the analytical stability analysis of unsymmetrically laminated structures. With the discrete plate theory, the stability of laminated structures can be reduced to single laminated plates. The structure is divided into individual segments, and the surrounding structure is modelled by rotational elastic restraints. The governing equations for single plates under specific boundary conditions can be solved exactly with Lévy-type solutions. In this study, Lévy-type solutions for the mentioned boundary conditions under biaxial compressive load is described for the classical laminated plate theory, the first-order shear deformation theory and the third-order shear deformation theory (TSDT). In addition to transverse shear, bending–extension couplings of unsymmetrical cross-ply and antisymmetrical angle-ply laminates are considered. For the implementation of boundary conditions for the rotational restraints in the context of TSDT, a new set of conditions is formulated. The investigation shows very good agreement of the buckling load with comparative finite element analyses for different layups. [ABSTRACT FROM AUTHOR]

In this study, an analytical solution based on the first-order shear deformation theory was performed for free vibration and buckling analysis of functionally graded porous beams (FGM-P) subjected to various boundary conditions. Also, this problem is solved by using finite element (FEM) and artificial neural network (ANN) methods. Here a Ritz-based analytical solution is used, and different polynomial series functions are proposed for each boundary condition. Lagrange's principle was used while deriving the equations of motion. A power-law rule describes the variation of the beam's materials in volume. The normalized fundamental frequencies and critical buckling loads are obtained for various boundary conditions, power-law index (k), slenderness (L/h), porosity coefficient (e), and porosity distribution (FGM-P1, FGM-P2). The polynomial series functions used in this study were verified with the literature, and the numerical results obtained were compared with FEM and ANN. The results obtained are quite compatible with each other. [ABSTRACT FROM AUTHOR]

This study aims to examine the effect of the diameter, number, and location of the circular cutout on the free vibration response and buckling loads of the laminated composites. Eigen-buckling and free vibrations analyses are performed for the laminated composite plates by using the finite element software ANSYS. Numerical results obtained by the finite element method are compared to the experimental ones. In the numerical analyses, the effect of the delamination around the cutout on the buckling load and the natural frequency is also examined. The critical buckling load and first natural frequency values obtained by both numerical and experimental studies are used to create a prediction model using the artificial neural networks. The Levenberg–Marquardt backpropagation algorithm is used as the training method. It is observed that both the number and location of the cutout affect the critical buckling load and first natural frequency values. Numerical and experimental results are presented together with the ANN prediction results. [ABSTRACT FROM AUTHOR]

A first endeavor is made in this paper to explore new analytic buckling solutions of moderately thick rectangular plates by a straightforward double finite integral transform method, with focus on typical non-Lévy-type fully clamped plates that are not easy to solve in a rigorous way by the other analytic methods. Solving the governing higher-order partial differential equations with prescribed boundary conditions is elegantly reduced to processing four sets of simultaneous linear equations, the existence of nonzero solutions of which determines the buckling loads and associated mode shapes. Both numerical and graphical results confirm the validity and accuracy of the developed method and solutions by favorable comparison with the literature and finite element analysis. The succinct but effective technique presented in this study can provide an easy-to-implement theoretical tool to seek more analytic solutions of complex boundary value problems. [ABSTRACT FROM AUTHOR]

This paper focuses on the buckling analysis of composite sandwich conical shells subjected to a uniform external lateral pressure based on the first-order shear deformation theory. Approximate analytical solutions are assumed to satisfy fully clamped boundary conditions and then Fourier decomposition and Galerkin method is applied to achieve closed-form relations of buckling loads. The closed analytical formula for the critical pressure has been verified by comparison with the finite-element solutions and a special case where the angle of the conical shell approaches zero, that is, a cylindrical shell. Based on this formula buckling analyses of sandwich conical shells with different types of core materials have been accomplished. The outcomes are achieved considering the effects of half-vertex cone angle, core thickness and indicating applicability, accuracy, and stability of the present method. [ABSTRACT FROM AUTHOR]

In order to avoid using C interpolation functions in finite element implementation of the previous zig-zag theories, artificial constraints, in which the first derivatives of transverse displacement will be replaced by the assumed variables, are usually employed. However, such assumption will violate continuity conditions of transverse shear stresses at interfaces. Differing from previous work, this paper will propose a C-type zig-zag theory for buckling analysis of laminated composite and sandwich plates with general configurations. The first derivatives of transverse displacement have been taken out from a displacement field of the proposed zig-zag theory. Thus, the C interpolation functions are only required in finite element implementations of the proposed model. Without use of any artificial constraints, an eight-node quadrilateral element based on the proposed model is presented by incorporating the terms associated with the geometric stiffness matrix. In order to verify performance of the proposed model, several buckling problems of sandwich plates with soft core have been analyzed. Numerical results show that the proposed model is able to predict accurately buckling loads of the soft-core sandwich plates with varying fiber orientations of face sheets. [ABSTRACT FROM AUTHOR]

A finite strain formulation is developed for elastic circular arches and rings in which the effects of shear deformations are included. Timoshenko beam hypothesis is adopted for incorporating shear. Finite strains are defined in terms of the normal and shear component of the longitudinal stretch. The constitutive relations for stress and finite strain are based on a hyperelastic constitutive model. Virtual work and equilibrium equations are derived. Closed-form in-plane buckling solutions are developed for circular rings and high arches under hydrostatic pressure. The effects of axial deformation prior to buckling as well as shear deformations are included in the buckling analysis. The formulation developed is compared with solutions in the literature and to the predictions of the finite element package ANSYS. The importance of including the effects of shear deformations for deep arches is investigated. [ABSTRACT FROM AUTHOR]

Making use of a mixed variational formulation based on the Green function of the substrate, which assumes as independent fields the structure displacements and the contact pressure, a simple and efficient finite element-boundary integral equation coupling method is derived and applied to the stability analysis of beams and frames resting on an elastic half-plane. Slender Euler-Bernoulli beams with different combinations of end constraints are considered. The examples illustrate the convergence to the existing exact solutions and provide new estimates of the buckling loads for different boundary conditions. Finally, nonlinear incremental analyses of rectangular pipes with compressed columns and free or pinned foundation ends are performed, showing that pipes stiffer than the soil may exhibit snap-through instability. [ABSTRACT FROM AUTHOR]