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A mathematical model for nonlocal vibration and buckling of embedded two-dimensional (2D) decagonal quasicrystal (QC) layered nanoplates is proposed. The Pasternak-type foundation is used to simulate the interaction between the nanoplates and the elastic medium. The exact solutions of the nonlocal vibration frequency and buckling critical load of the 2D decagonal QC layered nanoplates are obtained by solving the eigensystem and using the propagator matrix method. The present three-dimensional (3D) exact solution can predict correctly the nature frequencies and critical loads of the nanoplates as compared with previous thin-plate and medium-thick-plate theories. Numerical examples are provided to display the effects of the quasiperiodic direction, length-to-width ratio, thickness of the nanoplates, nonlocal parameter, stacking sequence, and medium elasticity on the vibration frequency and critical buckling load of the 2D decagonal QC nanoplates. The results show that the effects of the quasiperiodic direction on the vibration frequency and critical buckling load depend on the length-to-width ratio of the nanoplates. The thickness of the nanoplate and the elasticity of the surrounding medium can be adjusted for optimal frequency and critical buckling load of the nanoplate. This feature is useful since the frequency and critical buckling load of the 2D decagonal QCs as coating materials of plate structures can now be tuned as one desire. [ABSTRACT FROM AUTHOR]

A procedure of the method of reverberation ray matrix (MRRM) is developed to perform the buckling analysis of thin multi-span rectangular plates having internal line supports or stiffeners. A computation algorithm for the reverberation ray matrix in the MRRM is derived to determine the buckling loading. Specifically, the analytical solutions are presented for the buckling of the structure having two opposite simply-supported or clamped-supported edges with spans, while the constraint condition of two remaining edges may be in any combination of free, simply-supported, and clamped boundary conditions. Furthermore, based on the analysis of matrices relating to the unknown coefficients in the solution form for the deflection in terms of buckling modal functions, some recursive equations (REs) for the MRRM are introduced to generate a reduced reverberation ray matrix with unchanged dimension when the number of spans increases, which promotes the computation efficiency. Several numerical examples are given, and the present results are compared with the known solutions to illustrate the validity and accurateness of the MRRM for the buckling analysis. [ABSTRACT FROM AUTHOR]

The conventional approach to analysis the buckling of rectangular laminates containing an embedded delamination subjected to the in-plane loading is to simplify the laminate as a beam-plate from which the predicted buckling load decreases as the length of the laminate increases. Two-dimensional analyses are employed in this paper by extending the one-dimensional model to take into consideration of the influence of the delamination width on the buckling performance of the laminates. The laminate is simply supported containing a through width delamination. A new parameter β defined as the ratio of delamination length to delamination width is introduced with an emphasis on the influence of the delamination size. It is found that (i) when the ratio β is greater than one snap-through buckling prevails, the buckling load is determined by the delamination size and depth only; (ii) as the ratio β continues to increase, the buckling load will approach to a constant value. Solutions are verified with the well established results and are found in good agreement with the latter. [ABSTRACT FROM AUTHOR]

The governing equations of elasticity theory for natural vibration and buckling of anisotropic plate are derived from Hellinger-Reissner’s variational principle with nonlinear strain-displacement relations. Simply supported rectangular hybrid plates are studied with a precise integration method. This method, in contrast to the traditional finite difference approximation, gives highly precise numerical results that approach the full computer precision. So the results for natural vibration and stability of hybrid plates presented in the paper can be riewed as approximate analytical solutions. Furthermore, several types of coupling effects such as coupling between bending and twisting, and coupling between extension and bending, when the layer stacking sequence is asymmetric, are considered by only one set of governing equations. [ABSTRACT FROM AUTHOR]

The nonlinear vibration fundamental equation of circular sandwich plate under uniformed load and circumjacent load and the loosely clamped boundary condition were established by von Karman plate theory, and then accordingly exact solution of static load and its numerical results were given. Based on time mode hypothesis and the variational method, the control equation of the space mode was derived, and then the amplitude frequency-load character relation of circular sandwich plate was obtained by the modified iteration method. Consequently the rule of the effect of the two kinds of load on the vibration character of the circular sandwich plate was investigated. When circumjacent load makes the lowest natural frequency zero, critical load is obtained. [ABSTRACT FROM AUTHOR]

The graded multiweb structure of heterogeneous anisotropic materials, which makes full use of the continuous, gradual and changing physical mechanical performance of material properties, has a widespread application in aeroplane aerofoil structure and automobile lightweight structure. On the basis of laminate buckling theory, the equivalent rigidity method is adopted to establish the corresponding constitutive relation and the non-linear buckling governing equation for the graded multiweb structure. In finding the solution, the critical load of buckling under different complicated boundary conditions together with combined loads were obtained and testification of the experimental analysis shows that the calculation results can satisfy the requirements of engineering design in a satisfactory way. Results obtained from the research say that: graded materials can reduce the concentrated stress on the interface in an effective way and weaken the effect of initial defect in materials and thereby improve the strength and toughness of materials. [ABSTRACT FROM AUTHOR]

Cubic B-spline taken as trial function, the nonlinear bending of a circular sandwich plate was calculated by the method of point collocation. The support could be elastic. A sandwich plate was assumed to be Reissner model. The formulae were developed for the calculation of a circular sandwich plate subjected to polynomial distributed loads, uniformly distributed moments, radial pressure or radial prestress along the edge and their combination. Buckling load was calculated for the first time by nonlinear theory. Under action of uniformly distributed loads, results were compared with that obtained by the power series method. Excellences of the program written by the spline collocation method are wide convergent range, high precision and universal. [ABSTRACT FROM AUTHOR]