scholarly journals Dynamic Analysis of Thick Plates Including Deep Beams on Elastic Foundations Using Modified Vlasov Model

2013 ◽  
Vol 20 (1) ◽  
pp. 29-41 ◽  
Author(s):  
Korhan Ozgan
Keyword(s):  
Finite Element ◽  
Dynamic Analysis ◽  
Plate Theory ◽  
Beam Theory ◽  
Mindlin Plate ◽  
Element Formulation ◽  
Soil System ◽  
Stiffness Matrices ◽  
Foundation Model ◽  
Foundation Plate

Dynamic analysis of foundation plate-beam systems with transverse shear deformation is presented using modified Vlasov foundation model. Finite element formulation of the problem is derived by using an 8-node (PBQ8) finite element based on Mindlin plate theory for the plate and a 2-node Hughes element based on Timoshenko beam theory for the beam. Selective reduced integration technique is used to avoid shear locking problem for the evaluation of the stiffness matrices for both the elements. The effect of beam thickness, the aspect ratio of the plate and subsoil depth on the response of plate-beam-soil system is analyzed. Numerical examples show that the displacement, bending moments and shear forces are changed significantly by adding the beams.

scholarly journals A Kollár and Pluzsik anisotropic composite beam theory for arbitrary multicelled cross sections

2016 ◽  
Vol 35 (23) ◽  
pp. 1696-1711 ◽  
Author(s):  
Danilo S Victorazzo ◽  
Andre De Jesus
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Composite Beam ◽  
Linear Equations ◽  
Beam Theory ◽  
Element Formulation ◽  
Compliance Matrix ◽  
Asymmetric System ◽  
Anisotropic Composite ◽  
Stiffness Matrices

In this paper we extend Kollár and Pluzsik’s thin-walled anisotropic composite beam theory to include multiple cells with open branches and booms, and present a finite element formulation utilizing the stiffness matrix obtained from this theory. To recover the 4 × 4 compliance matrix of a beam containing N closed cells, we solve an asymmetric system of 2N + 4 linear equations four times with unitary section loads and extract influence coefficients from the calculated strains. Finally, we compare 4 × 4 stiffness matrices of a multicelled beam using this method against matrices obtained using the finite element method to demonstrate accuracy. Similarly to its originating theory, the effects of shear deformation and restrained warping are assumed negligible.

Conforming shear-locking-free four-node rectangular finite element of moderately thick plate

2016 ◽  
Vol 25 (5-6) ◽  
pp. 141-152
Author(s):  
Ivo Senjanović ◽  
Marko Tomić ◽  
Smiljko Rudan ◽  
Neven Hadžić
Keyword(s):  
Finite Element ◽  
Thick Plate ◽  
Plate Theory ◽  
Shear Stiffness ◽  
Mindlin Plate ◽  
Shear Locking ◽  
Shape Functions ◽  
Beam Shape ◽  
Stiffness Matrices ◽  
Moderately Thick Plate

AbstractAn outline of the modified Mindlin plate theory, which deals with bending deflection as a single variable, is presented. Shear deflection and cross-section rotation angles are functions of bending deflection. A new four-node rectangular finite element of moderately thick plate is formulated by utilizing the modified Mindlin theory. Shape functions of total (bending+shear) deflections are defined as a product of the Timshenko beam shape functions in the plate longitudinal and transversal direction. The bending and shear stiffness matrices, and translational and rotary mass matrices are specified. In this way conforming and shear-locking-free finite element is obtained. Numerical examples of plate vibration analysis, performed for various combinations of boundary conditions, show high level of accuracy and monotonic convergence of natural frequencies to analytical values. The new finite element is superior to some sophisticated finite elements incorporated in commercial software.

A Nonclassical Finite Element Approach for the Nonlinear Analysis of Micropolar Plates

2016 ◽  
Vol 12 (1) ◽  
Author(s):  
R. Ansari ◽  
A. H. Shakouri ◽  
M. Bazdid-Vahdati ◽  
A. Norouzzadeh ◽  
H. Rouhi
Keyword(s):  
Finite Element ◽  
Plate Theory ◽  
Nonlinear Modeling ◽  
Three Dimensional ◽  
Mindlin Plate ◽  
Small Scale ◽  
Element Formulation ◽  
Nonlinear Bending ◽  
Finite Element Approach ◽  
Element Approach

Based on the micropolar elasticity theory, a size-dependent rectangular element is proposed in this article to investigate the nonlinear mechanical behavior of plates. To this end, a novel three-dimensional formulation for the micropolar theory with the capability of being used easily in the finite element approach is developed first. Afterward, in order to study the micropolar plates, the obtained general formulation is reduced to that based on the Mindlin plate theory. Accordingly, a rectangular plate element is developed in which the displacements and microrotations are estimated by quadratic shape functions. To show the efficiency of the developed element, it is utilized to address the nonlinear bending problem of micropolar plates with different types of boundary conditions. It is revealed that the present finite element formulation can be efficiently employed for the nonlinear modeling of small-scale plates by considering the micropolar effects.

Application of Composite Plate Theory and the Finite Element Method to the Dynamics and Stress Analysis of Spatial Flexible Mechanical Systems

1994 ◽  
Vol 116 (3) ◽  
pp. 952-960 ◽  
Author(s):  
J. M. Kremer ◽  
A. A. Shabana ◽  
G. E. O. Widera
Keyword(s):  
Finite Element ◽  
Rigid Body ◽  
Stress Analysis ◽  
Arbitrary Number ◽  
Plate Theory ◽  
Mass Matrix ◽  
Composite Plates ◽  
The Body ◽  
Element Formulation ◽  
Stiffness Matrices

This investigation concerns itself with the dynamic and stress analysis of thin, laminated composite plates consisting of layers of orthotropic laminae. It is assumed that the bonds between the laminae are infinitesimally thin and shear nondeformable. The finite element formulation presented is sufficiently general to accept an arbitrary number of layers and an arbitrary number of orthotropic material property sets. In the dynamic formulation presented, the laminae is assumed to undergo large arbitrary rigid body displacements and small elastic deformations. The nodal shape functions of the laminae are assumed to have rigid body modes that need to describe only large rigid body translations. Using the expressions for the kinetic and strain energies, the lamina mass and stiffness matrices are identified. The nonlinear mass matrix of the lamina is expressed in terms of a set of invariants that depend on the assumed displacement field. By summing the laminae kinetic and strain energies, the body mass and stiffness matrices are identified. It is shown that the body invariants can be expressed explicitly in terms of the invariants of its laminae. Numerical examples of a spatial RSSR mechanism are presented in order to demonstrate the use of the present formulation.

Dynamic Analysis of Plates with Cut-Out Carrying Concentrated and Distributed Mass

2020 ◽  
Vol 162 (A3) ◽  
Author(s):  
S Pal ◽  
S Haldar ◽  
K Kalita
Keyword(s):  
Finite Element ◽  
Dynamic Analysis ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Element Formulation ◽  
Plate Bending ◽  
Mass Lumping ◽  
First Order ◽  
Side Ratio ◽  
Isotropic Plates

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.

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