A differential quadrature nonlinear free vibration analysis of laminated composite skew thin plates
TL;DR: Using a differential quadrature (DQ) method, large amplitude free vibration analysis of laminated composite skew thin plates is presented in this paper, where the governing equations are based on the thin plate theory (TPT) and the geometrical nonlinearity is modeled using Green's strain in conjunction with von Karman assumptions.
Abstract: Using a differential quadrature (DQ) method, large amplitude free vibration analysis of laminated composite skew thin plates is presented The governing equations are based on the thin plate theory (TPT) and the geometrical nonlinearity is modeled using Green's strain in conjunction with von Karman assumptions To cause the impact due to nonlinear terms more significant, in-plane immovable simply supported, clamped and different combinations of them are considered The effects of different parameters on the convergence and accuracy of the method are studied The resulted solutions are compared to those from other numerical methods to show the accuracy of the method Some new results for laminated composite skew plates with different mixed boundary conditions are presented and are compared with those obtained using the first order shear deformation theory based DQ (FSDT-DQ) method Excellent agreements exist between the solutions of the two approaches but with much lower computational efforts of the present DQ methodology with respect to FSDT-DQ method
Citations
More filters
387 citations
TL;DR: In this paper, the free vibration analysis of multilayered laminated composite and sandwich plates using various methods available for the analysis of plates is presented and compared with other higher order shear deformation theories.
284 citations
Cites methods from "A differential quadrature nonlinear..."
...Differential quadrature method was presented by Malekzadeh [248] to study the free vibration analysis of laminated composite skew thin plates....
[...]
TL;DR: In this paper, the surface and nonlocal effects on the nonlinear flexural free vibrations of elastically supported non-uniform cross section nanobeams are studied simultaneously using Hamilton's principle in conjunction with Eringen's nonlocal elasticity theory.
Abstract: The surface and nonlocal effects on the nonlinear flexural free vibrations of elastically supported non-uniform cross section nanobeams are studied simultaneously. The formulations are derived based on both Euler–Bernoulli beam theory (EBT) and Timoshenko beam theory (TBT) independently using Hamilton’s principle in conjunction with Eringen’s nonlocal elasticity theory. Green’s strain tensor together with von Karman assumptions are employed to model the geometrical nonlinearity. The differential quadrature method (DQM) as an efficient and accurate numerical tool in conjunction with a direct iterative method is adopted to obtain the nonlinear vibration frequencies of nanobeams subjected to different boundary conditions. After demonstrating the fast rate of convergence of the method, it is shown that the results are in excellent agreement with the previous studies in the limit cases. The influences of surface free energy, nonlocal parameter, length of non-uniform nanobeams, variation of nanobeam width and elastic medium parameters on the nonlinear free vibrations are investigated.
166 citations
TL;DR: In this article, free vibration analysis of initially stressed simply supported functionally graded curved panel resting on two-parameter elastic foundation (Pasternak model), subjected in thermal environment is studied using the three-dimensional elasticity formulation.
105 citations
TL;DR: In this paper, a variational differential quadrature (VDQ) method is proposed to discretize the energy functional in the structural mechanics, which is based on the accurate and direct discretization of energy functional.
90 citations
References
More filters
Book•
01 Jan 1997
TL;DR: In this paper, the authors present a one-dimensional analysis of fiber-reinforced composite materials and their properties, including the properties of the components of a Lamina and their relationship with other components.
Abstract: Introduction and Mathematical Preliminaries Fiber-Reinforced Composite Materials. Vectors and Tensors. Matrices. Transformation of Vector and Tensor Components. Integral Relations. Equations of Anisotropic Elasticity Classification of Equations. Kinematics. Kinetics. Constitutive Equations. Equations of Thermoelasticity and Electroelasticity. Summary. Virtual Work Principles and Variational Methods Virtual Work. The Variational Operator and Functionals. Extrema of Functionals. Virtual Work Principles. Variational Methods. Summary. Introduction to Composite Materials Basic Concepts and Terminology. Constitutive Equations of a Lamina. Transformation of Stresses and Strains. Plane Stress Constitutive Relations. Classical and First-Order Theories of Laminated Composite Plates Introduction. An Overview of ESL Laminate Theories. The Classical Laminated Plate Theory. The First-Order Laminated Plate Theory. Stiffness Characteristics for Selected Laminates. One-Dimensional Analysis of Laminated Plates Introduction. Analysis of Laminated Beams Using CLPT. Analysis of Laminated Beams Using FSDT. Cylindrical Bending Using CLPT. Cylindrical Bending Using FSDT. Closing Remarks. Analysis of Specially Orthotropic Plates Using CLPT Introduction. Bending of Simply Supported Plates. Bending of Plates with Two Opposite Edges Simply Supported. Bending of Rectangular Plates with Various Boundary Conditions. Buckling of Simply Supported Plates Under Compressive Loads. Buckling of Rectangular Plates Under Inplane Shear Load. Vibration of Simply Supported Plates. Buckling and Vibration of Plates with Two Parallel Edges Simply Supported. Closure. Analytical Solutions of Rectangular Laminates Using CLPT Governing Equations in Terms of Displacements. Admissible Boundary Conditions for the Navier Solutions. Navier Solutions of Antisymmetric Cross-Ply Laminates. The Navier Solutions of Antisymmetric Angle-Ply Laminates. The LTvy Solutions. Analysis of Midplane Symmetric Laminates. Transient Analysis. Summary. Analytical Solutions of Rectangular Laminates Using FSDT Introduction. Simply Supported Antisymmetric Cross-Ply Laminates. Simply Supported Antisymmetric Angle-Ply Laminates. Antisymmetric Cross-Ply Laminates with Two Opposite Edges Simply Supported. Antisymmetric Angle-Ply Laminates with Two Opposite Edges Simply Supported. Transient Solutions. Summary. Finite Element Analysis of Composite Laminates Introduction. Laminated Beams and Plate Strips by CLPT. Timoshenko Beam/Plate Theory. Numerical Results for Beams and Plate Strips. Finite Element Models of Laminated Plates (CLPT). Finite Element Models of Laminated Plates (FSDT). Summary. Refined Theories of Laminated Composite Plates Introduction. A Third-Order Plate Theory. Higher-Order Laminate Stiffness Characteristics. The Navier Solutions. LTvy Solutions of Cross-Ply Laminates. Displacement Finite Element Model. Layerwise Theories and Variable Kinematic Models In troduction. Development of the Theory. Finite Element Model. Variable Kinematic Formulations. Nonlinear Analysis of Composite Laminates Introduction. Nonlinear Stiffness Coefficients. Solution Methods for Nonlinear Algebraic Equations. Computational Aspects and Numerical Examples. Closure. Index Most chapters include Exercises and References for Additional Reading
1,344 citations
TL;DR: The differential quadrature method (DQM) as discussed by the authors is a numerical solution technique for initial and/or boundary problems, which was developed by the late Richard Bellman and his associates in the early 70s.
Abstract: The differential quadrature method is a numerical solution technique for initial and/or boundary problems. It was developed by the late Richard Bellman and his associates in the early 70s and, since then, the technique has been successfully employed in a variety of problems in engineering and physical sciences. The method has been projected by its proponents as a potential alternative to the conventional numerical solution techniques such as the finite difference and finite element methods. This paper presents a state-of-the-art review of the differential quadrature method, which should be of general interest to the computational mechanics community.
1,217 citations
TL;DR: In this paper, the complementary energy method is applied to the free vibration analysis of various structural components, including prismatic and tapered bars, prismatic beams, and axisymmetric motion of circular membranes.
Abstract: Two approximate methods, which have not previously been used for structural dynamics problems, are applied to the free vibration analysis of various structural components. The first method is a new version of the complementary energy method. It is shown to be considerably more accurate than the conventional Rayleigh and Rayleigh-Schmidt methods when applied to spatially one-dimensional free vibration problems: prismatic and tapered bars, prismatic beams, and axisymmetric motion of circular membranes. The second method is the differential quadrature method introduced by Bellman and his associates. It is applied successfully here to all of the problems mentioned plus square membranes and circular and square plates.
307 citations
TL;DR: In this article, the behavior of thin, rectangular, orthotropic elastic plates, with immovable edges and undergoing large deflections, is investigated by the numerical technique of differential quadrature.
Abstract: The behavior of thin, rectangular, orthotropic elastic plates, with immovable edges and undergoing large deflections, is investigated by the numerical technique of differential quadrature. Approximate results are obtained, using the Newton-Raphson method and, alternatively, a finite-difference-based method to solve the nonlinear systems of equations. Bending stresses, membrane stresses, and deflections are calculated for plates with fully clamped and simply supported flexural edge conditions under uniform pressure loading. Results are compared with existing analytical, numerical, and experimental ones. The present method gives good accuracy and is computationally efficient.
157 citations
TL;DR: In this article, the authors presented a computationally efficient and an accurate new methodology in differential quadrature analysis of beam elements, which would overcome the difficulties in boundary conditions implementations of fourth-order differential equations encountered in such problems.
129 citations