Showing 5 results for First-Order Shear Deformation
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Volume 13, Issue 12 (2-2014)
Abstract
In this study, nonlinear bending analysis of ring-stiffened annular laminated composite plates is studied. A discretely stiffened plate theory for elastic large deflection analysis of uniformly distributed loaded is introduced. The governing equations are derived based on a first-order shear deformation plate theory (FSDT) and large deflection von Karman equations. The numerical results are obtained using the dynamic relaxation (DR) method combined with the central finite difference discretization technique. For this purpose, a FORTRAN computer program is developed to generate the numerical results. In order to verify the accuracy of the present method the results are compared with those available in the literatures and ABAQUS finite element package as well. The computer code can handle symmetric, unsymmetrical and general theta-ply schemes. The effects of the plate thicknesses, different ratio of outer to inner radius, depth of stiffener, boundary condition and laminates lay-up are studied in detail.
Ali Bakhsheshy, Hossein Mahbadi,
Volume 17, Issue 3 (5-2017)
Abstract
Viscoelasticity is a property of materials that exhibit both viscous and elastic characteristics. In linear viscoelasticity, the stress is linearly related to the history function of strain. This paper discusses vibration analysis of functionally graded viscoelastic rectangular plate. The viscoelastic behavior of the plate is modeled using the Zener three-parameter model. Also, the material properties of the plate are graded through the thickness according to the volume fraction model. The maximum stress and strain are calculated based on the linear first-order shear deformation theory and the simply support boundary conditions is assumed at all four edges of the plate. A code is prepared using the Mathematica software to obtain the frequency values and effect of inherent and geometric characteristics of the sheet on natural frequency of the plate. These effects are studied using the tables and graphs represented in the results and discussion section of the paper. The results obtained in this paper are simplified to a functionally elastic plate to compare with those given in the literature search. The comparison of results shows good agreement against data given in literature for both cases.
Ali Asghar Masoumi, Gholam Hossein Rahimi, Gholam Hosain Liaghat,
Volume 17, Issue 6 (8-2017)
Abstract
In this paper, numerical and analytical solution of composite metal cylindrical vessel are investigated under dynamic load using first-order shear deformation theory and differential quadrature method. For this purpose, the shell equilibrium equations are derived based on the first order shear deformation theory. The load applied to the shell is achieved from the experimental test of a double-base propellant and then, is applied to the model in numerical and theoretical analysis. The aim of this paper is study and investigate the behavior of the composite metal cylindrical vessel under dynamic load with first-order shear deformation theory and comparing its results with the numerical solution. Therefore, after extracting the shell equilibrium equations are used from differential quadrature method for solve the equations. Then, the governing equations are extracted in a composite metal cylindrical vessel to form the matrix equations to solve with differential quadrature method. To apply boundary conditions from free and support clamping conditions are used and the results of these two modes are compared together. The MATLAB programming code is used to solve differential quadrature equations. To validate theoretical results, modeling and numerical analysis done by Abaqus finite element software and then, results are compared with the analytical solution using the differential quadrature method.
Ali Talezadehlari, G. H. Rahimi,
Volume 17, Issue 11 (1-2018)
Abstract
In this paper, axial buckling of a composite cylindrical shell with and without a rectangular cutout is studied based on the first-order shear deformation theory. The equations are derived in a general form and can be converted to Donnell`s, Love`s, and Sanders` theories. To investigate the perforated shell, a physical domain is decomposed into several elements with uniform boundary and loading conditions in each element edges. In each element, the governing equations are discretized in both longitudinal and circumferential directions by the use of generalized differential quadrature method (GDQM). By assembling these discretized relations, a system of algebraic equations is generated. The boundary conditions at the shell and cutout edges, and the compatibility conditions at the interface boundaries of adjacent elements are also discretized by GDQM. Finally, the buckling load is calculated by an eigenvalue solution. To validate the presented method, the results of GDQM are compared with the available ones in the literature and also with ABAQUS finite element model. Then a parametric analysis is performed to investigate the effects of different parameters on the buckling behavior of the shells with and without cutouts. This study illustrates that the shell layup has a great effect on the buckling load of a shell. In addition, the influence of increasing the cutout size is not identical for different layups. However, the buckling behavior is independent of the shell material. Moreover, it was concluded that the shell with a square cutout has higher critical load than the one with a rectangular opening.
E. Torkan, M. Pirmoradian, M. Hashemian,
Volume 19, Issue 9 (9-2019)
Abstract
In this paper, the dynamic stability of a moderately thick rectangular plate carrying an orbiting mass and lying on a visco-elastic foundation is studied. Considering all inertial terms of the moving mass and using plate first-order shear deformation theory, the governing equations on the dynamic behavior of the system are derived. The Galerkin’s method on the basis of trigonometric shape functions is applied to change the coupled governing partial differential equations to a system of ordinary differential equations. Due to the alternative motion of the mass along the circular path over the plate’s surface, the governing equations are the equations with the periodic constant. Applying the semi-analytical incremental harmonic balance method, the influences of the relative thickness of the plate, radius of the motion path, and stiffness and damping of the visco-elastic foundation on the instability conditions of the system are investigated. A good agreement can be observed by comparing the predicted results of the incremental harmonic balance method with the numerical solution results. Based on the findings, increasing the radius of the motion path broadens the instability regions. Moreover, increasing the stiffness and damping of the foundation cause the system more stable.
