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This work presents highly accurate numerical calculations of the buckling loads for thin elastic rectangular plates with known constant in-plane stresses, and in-plane shear loading that is increased until the critical load is obtained and the plate losses its stability. The solutions are obtained using the multi-term extended Kantorovich method. The solution is sought as the sum of multiplications of two one-dimensional functions. In this method a solution is assumed in one direction of the plate, and this enables transformation of the partial differential equation of the plate equilibrium into a system of ordinary differential equations. These equations are solved exactly by the exact element method, and an approximate buckling load is obtained. In the second step, the derived solution is now taken as the assumed solution in one direction, and the process is repeated to find an improved buckling load. This process converges with a small number of solution cycles. For shear buckling this process can only be used if two or more terms are taken in the expansion of the solution. Many examples are given for shear buckling loads for various cases of tension and compression bi-directional loading.

This paper presents a highly accurate method for analyzing the critical shear buckling load of thin elastic rectangular plates. The solutions are approximated by the extended spline collocation method (SCM). Using the quintic table in place of the complex quintic B-spline functions, one can easily formulate the field equation of shear buckling loads for a thin elastic rectangular plate. Through the generalized eigenvalue analysis, the shear buckling loads and mode shapes for the plate can be determined precisely. Numerical examples are given for the critical shear buckling load of plates with various combinations of boundary conditions, aspect ratios, and uni- and bi-directional compressive/tensile loadings. The solutions obtained by the SCM are compared with those by the finite element method, the Lagrangian multiplier method, and the extended Kantorovich method under several types of boundary conditions. Compared with the other methods, the proposed SCM is not only more accurate, but also easier for computation.

The stability characteristics of shear deformable trapezoidal composite plates are studied here. Thestrain smoothing technique is employed to approximate the membrane strains and curvatures of the edge-based smoothing cells. The transverse shear strains within the Reissner–Mindlin quadrilateral element are obtained using the edge-consistent interpolation approach. At the beginning, the performance of the present numerical technique is examined for the buckling analysis of trapezoidal panels under in-plane compressive or shear stresses. Thereafter, new results on the buckling and postbuckling behaviors of trapezoidal composite plates are presented, for which comparable numerical results are rare in the literature. Representative numerical results are presented to highlight the interaction between the higher pre-buckling stresses and increased stiffness near the shorter edge with fiber orientation and loading direction on the buckling resistance of trapezoidal panels.

A first attempt is made in this paper to explore new analytic shear buckling solution of clamped rectangular thin plates by a two-dimensional generalized finite integral transform method. The problem is classical but challenging due to the mathematical difficulty in handling the complex boundary value problem of the governing higher-order partial differential equation (PDE). Taking the vibrating beam functions as the integral kernels, and imposing the double transform, the problem comes down to solving a system of linear algebraic equations, thereby the analytic solution is obtained in a straightforward way. The present method is confirmed to be highly accurate with fast convergence, which agrees very well with both the finite element method (FEM) and energy method from the literature. The new analytic solution obtained may serve as a benchmark for validating other numerical and approximate methods.

In this paper, the isogeometric method is developed to study mechanical buckling behavior of nanocomposite plates reinforced by graphene sheets with temperature-dependent (TD) material properties in thermal environment. The plate is separately subjected to in-plane uniaxial, biaxial and shear loadings. It is assumed that the plate has different number of layers. By considering different volume fraction for each layer of graphene sheets, different functionally graded (FG) patterns of graphene sheets may be achieved. Furthermore, in some cases, it is considered that more than one FG patterns exist along the plate thickness. The energy statement of the plate is obtained using a logarithmic higher-order shear deformation theory (HSDT). Then, the isogeometric method is used to establish the desired eigenvalue problem. The comparison and convergence studies are presented for a wide range of numerical examples in all considered cases to show the correctness and ability of the solution. Afterwards, by presenting a set of numerical examples, the effects of plate significant parameters on the critical buckling load of the plate are examined. It is shown that the highest critical buckling loads occur when the plate has the minimum number of layers.

This paper deals with the shear strength of prestressed concrete box girders having corrugated steel webs (PCBGCSW), with particular emphasis on the shear lag and the stochastic variation of material properties. First, the shear strength curve of corrugated steel web is proposed based on experimental and analytical results obtained for simply supported beams composed of corrugated steel web without and with concrete flanges. In order to evaluate the shear strength of PCBGCSW based on the shear strength curve of corrugated steel web, it is important to know the distribution of shearing force between the corrugated steel web and the concrete flanges. The effect of the concrete flanges, therefore, on the distribution of shearing force is investigated considering the shear lag behavior. Finally the stochastic variation of material properties for the evaluation of the shear strength of corrugated steel webs is discussed from the design viewpoint.

The prestressed concrete composite girder bridge with corrugated steel webs is a new type of bridge structure which has been widely applied in domestic in recent years. In order to meet the practical engineering requirement on the large height with corrugated steel webs, the type 2400 corrugated steel webs was preliminary designed on the geometry parameters based on the original types of corrugated steel webs. The development of the elastic shear buckling strength theory for corrugated steel webs and the corresponding calculation method were concluded. A reliable finite element model for the elastic shear buckling analysis of corrugated steel webs was established. According to the numerical results obtained by finite element analysis of the elastic shear buckling of the type 2400 corrugated steel webs, the theoretical formulas for local elastic shear buckling strength and global elastic shear buckling strength were corrected, and empirical calculation formulas for interactive elastic shear buckling strength was obtained through fitting.