Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates

Exact solutions are derived for three-dimensional, anisotropic, linearly magneto-electroelastic, simply-supported, and multilayered rectangular plates under static loadings. While the homogeneous solutions are obtained in terms of a new and simple formalism that resemble the Stroh formalism, solutions for multilayered plates are expressed in terms of the propagator matrix. The present solutions include all the previous solutions, such as piezoelectric, piezomagnetic, purely elastic solutions, as special cases, and can therefore serve as benchmarks to check various thick plate theories and numerical methods used for the modeling of layered composite structures. Typical numerical examples are presented and discussed for layered piezoelectric/piezomagnetic plates under surface and internal loads.

https://blogs.uakron.edu/ernianpan/files/2014/09/046_2001JAMPanMEESimpleSupport.pdf

Exact Solution for Simply Supported and Multilayered Magneto-Electro-Elastic Plates

Three-dimensional exact solution for the vibration of functionally graded rectangular plates

An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates

Static deformations, and free and forced vibrations of a thick rectangular functionally graded elastic plate are analyzed by using a higher-order shear and normal deformable plate theory (HOSNDPT) and a meshless local Petrov–Galerkin (MLPG) method. All components of the stress tensor are computed from equations of the plate theory. The plate material, made of two isotropic constituents, is assumed to be macroscopically isotropic with material properties varying in the thickness direction only. Effective material moduli are computed by using the Mori–Tanaka homogenization technique. Computed results for static and free vibration problems are found to agree well with their analytical solutions. The response of the plate to impulse loads is also computed for different volume fractions of the two constituents. Contributions of the work include the use of the HOSNDPT and the MLPG method for the analysis of functionally graded plates.

Static and dynamic deformations of thick functionally graded elastic plates by using higher-order shear and normal deformable plate theory and meshless local Petrov -Galerkin method

A three-dimensional, linear, small deformation theory of elasticity solution by the direct method is given for the flexure of simply supported homogeneous, isotropic, thick rectangular plates under arbitrary loading. This solution, in terms of infinite series is formally exact and yields accurate numerical results without undue effort. Numerical results are presented for uniformly distributed normal load on the top surface. The results from Reissner's theory of thick plates and the predictions of thin plate theory are compared with the values from the present exact solution. The analysis is readily extended for laminated plates of isotropic materials. Numerical results are also given for a three-ply laminate under uniformly distributed normal load on the top surface, and are used to assess the accuracy of thin plate theory predictions for laminates.



Fur das Biegeproblem einer einfach unterstutzten, homogenen, isotropen, dicken, beliebig belasteten Rechteckplatte wird auf direktem Wege uber eine dreidimensionale lineare Theorie kleiner elastischer Verformungen eine Losung gewonnen. Sie erscheint in der Gestalt unendlicher Reihen, ist formal exakt und liefert ohne unzumutbaren Aufwand genaue numerische Resultate. Solche werden fur den Fall einer uber die obere Randflache gleichformig verteilten Normallast angegeben und mit den Ergebnissen der Reissnerschen Theorie dicker Platten und mit den Voraussagen einer Theorie dunner Platten verglichen. Die verwendete Analysis last sich leicht auf geschichtete Platten aus isotropen Materialien ausdehnen. Fur eine Dreischichtplatte, auf deren obere Randflache eine gleichformig verteilte Normallast wirkt, werden die numerischen Ergebnisse mitgeteilt und dazu benutzt, die Genauigkeit der von der Theorie dunner Platten gemachten Voraussagen einzuschatzen.

S. Srinivas

Papers

Flexure of Simply Supported Thick Homogeneous and Laminated Rectangular Plates