ANALYSIS OF SYMMETRIC LAMINATED RECTANGULAR PLATES IN PLANE STRESS

Symmetric laminated plates used usually are anisotropic plates. Based on the fundamental equation for anisotropic rectangular plates in plane stress problem, a general analytical solution is established accurately by method of stress function. Therefore the general formula of stress and displacement in plane is given. The integral constants in general formula can be determined by boundary conditions. This general solution is composed of solutions made by trigonometric function and hyperbolic function, which can satisfy the problem of arbitrary boundary conditions along four edges, and the algebraic polynomial solutions which can satisfy the problem of bonndary conditions at four corners. Consequently this general solution can be used to solve the plane stress problem with arbitrary boundary conditions. For example, a symmetric laminated square plate acted with uniform normal load, tangential load and nonuniform normal load on four edges is calculated and analyzed.

Snapthrough response of an innovative symmetric bistable composite wing

This study presents a numerical investigation into the equilibrium shapes and snapthrough response of an innovative bistable symmetric composite wing.The proposed design is a compound plate that consists of a symmetric flat platform followed by a winglet that utilizes the modified hybrid bistable symmetric laminate recently developed in the reference.The hybrid layup of the winglet resolves the issue of losing the bistability of the unsymmetric laminate when attached to another structure.An approximate analytical model based on the Rayleigh-Ritz method is developed for the compound plate that considers the geometric nonlinearity,the clamping conditions at the wing root,and the compatibility conditions at the interface.The static equilibrium positions predicted by the model were verified against the ABAQUS finite element(FE)results and an excellent agreement was obtained.The influence of the geometrical and material parameters of the proposed design on the static equilibrium shapes and the snapthrough response was examined.The following parameters were considered:the length ratio of the flat plate to the bistable winglet,the thickness and location of the bidirectional glass epoxy layers,the load location,and the wing’s taperness and aspect ratio.All parameters were found significant,and their effects were discussed.The novelty of this work is that it presents the equilibrium shapes and the snapthrough response of a bistable laminate as a part of a bigger compliant structure,which mimics the scenario in real-life applications.

Control Mechanism of Surface Subsidence and Overburden Movement in Backfilling Mining based on Laminated Plate Theory

The backfilling mining technology is a type of high-efficiency coal mining technology that is used to address the environmental issues caused by the caving mining technology.In this paper,the mechanical model of symmetrical laminated plate representing the overburden movement caused by the backfilling mining technology is established,and the governing differential equation of the motion of the overburden is derived.The boundary conditions of the mechanical model are put forward,and the analytical solution of the overburden movement and surface subsidence is obtained.The numerical model of the overburden movement and surface subsidence,under mining with backfilling,is established by means of the FLAC3D numerical software,which aims to systematically study the influence of backfilling compactness,mining thickness,and mining depth on the overburden movement and surface subsidence in backfilling mining.When the compactnessηis less than 70%,the overburden movement and surface subsidence is greater,while whenηis greater than 70%,the overburden movement and surface subsidence is reduced significantly.On this basis,the control mechanism of surface subsidence and overburden movement in backfilling mining is obtained.The suitable backfilling compactness is the key to controlling surface subsidence and overburden movement in backfilling mining.

Modeling vibration behavior of delaminated composite laminates using meshfree method in Hamilton system

Free vibration analysis of composite laminates with delaminations is performed based on a three-dimensional semi-analytical model established by introducing the local radial point interpolation method（LRPIM） into a Hamilton system. The governing equation is derived with a transfer matrix technique and a spring layer model based on a local weak-form equivalent to the modified Hellinger-Reissner variational principle. Main superiority of the present model is that the scale of the governing equation involves only the so-called state variables at the top and bottom surfaces, and is insensitive to the thickness and the layer number of the composite laminates. Several numerical examples for analyzing the vibration frequencies and mode shapes of delaminated composite beams and plates are given to validate the model. The results are in good agreement with the pre-existing results.