Impulse deformation of triangular plates based on the classical theory

This article discusses the impulse effects of various loads on triangular, isosceles, elastic, isotropic plates. Analytical solutions of the direct problem of determining the internal moments and deflections of the plate, as well as the numerical results of calculations of specific loading case are presented. Goal. The goal is to develop a method for solving direct problems of determining internal moments and deflections in rectangular triangular, isosceles, elastic, thin, isotropic plates. Methodology. To solve the direct problem, the Navier method, the classical theory of modeling vibrations of thin plates and the Laplace transform are used. Results. A technique has been obtained that allows one to obtain numerical and analytical dependences for calculating the internal moments and deflections in a triangular plate. Originality. For the first time, a technique was developed for solving direct non-stationary problems to determine the internal moments and deflections in rectangular triangular, isosceles, elastic, thin, isotropic plates based on the classical theory. Practical value. The obtained analytical dependences can be used to simulate impulse vibrations of square and isosceles rectangular triangular thin isotropic elastic plates, which can be critical structural elements.

DYNAMIC ANALYSIS OF PLATES WITH CUT-OUT CARRYING CONCENTRATED AND DISTRIBUTED MASS

An isoparametric plate bending element with nine nodes is used in this paper for dynamic analysis of isotropic cut-out plate having concentrated and uniformly distributed mass on the plate. The Mindlin’s first-order shear deformation theory (FSDT) is used in the present finite element formulation. Two proportionate mass lumping schemes are used. The effect of rotary inertia is included in one of the mass lumping schemes in the present element formulation. Dynamic analysis of rectangular isotropic plates with cut-out having different side ratio, thickness ratio and boundary condition is analysed using a finite element method. The present results are compared with the published results. Some new results on isotropic plates with cut-out having different side ratio, ratio of side-to-thickness of the plate, different position and size of cut-out in plates subjected to transversely concentrated and distributed mass are presented.

Application of generalized equations of finite difference method to computation of bent isotropic stretched and/or compressed plates of variable stiffness under elastic foundation

The computation of bent isotropic plates, stretched and/or compressed, is a topic widely explored in the literature from both experimental and numerical point of view. We expose in this work an application of the generalized equations of Finite difference method to that topic. The strength of the proposed method is the ability to reconstruct the approximate solution with respect of eventual discontinuities involved in the investigated function as well as its first and second derivatives, including the right-hand side of the equilibrium equation. It is worth mentioning that by opposition to finite element methods our method needs neither fictitious points nor a special condensation of grid. Well-known benchmarks are used in this work to illustrate the efficiency of our numerical and the high accuracy of calculation as well. A comparison of our results with those available in the literature also shows good agreement.

Free Vibration Analysis of Thick Isotropic Plate by Using 5th Order Shear Deformation Theory

In the present study, a 5th order shear deformation theory (5th OSDT) is presented for free vibration analysis of simply supported thick isotropic plates. Governing equations and boundary conditions are evaluated using the concept of virtual work. Numerical results for free vibration analysis include the effects of side to thickness and plate aspect ratios for simply supported thick isotropic plates. Non-dimensional bending mode frequencies, non-dimensional thickness shear mode frequencies and non-dimensional thickness stretch mode frequencies are obtained. Closed form analytical solutions for simply supported isotropic thick plates subjected to single sinusoidal distributed loads are obtained for comparison purpose. The problems considered in this study are solved using MATLAB software. Non-dimensional bending frequencies and non-dimensional thickness shear mode frequencies obtained through the 5th OSDT match well with the exact analytical and exponential shear deformation theory (ESDT) results. Further, the non-dimensional thickness stretch mode frequencies are found to be imaginary.