Topic
Plate theory
About: Plate theory is a research topic. Over the lifetime, 8571 publications have been published within this topic receiving 242295 citations.
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TL;DR: In this article, three-dimensional elasticity solutions for rectangular laminates with pinned edges are constructed for three dimensional elasticity problems, including a sandwich plate, and compared to the analogous results in classical laminated plate theory.
Abstract: In a continuing study, three-dimensional elasticity solutions are constructed for rectangular laminates with pinned edges. The lamination geometry treated consists of arbitrary numbers of layers which can be isotropic or orthotropic with material symmetry axes parallel to the plate axes. Several specific example problems are solved, including a sandwich plate, and compared to the analogous results in classical laminated plate theory.
1,730 citations
TL;DR: In this paper, Navier's solutions of rectangular plates, and finite element models based on the third-order shear deformation plate theory are presented for the analysis of through-thickness functionally graded plates.
Abstract: Theoretical formulation, Navier's solutions of rectangular plates, and finite element models based on the third-order shear deformation plate theory are presented for the analysis of through-thickness functionally graded plates. The plates are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity of the plate is assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents. The formulation accounts for the thermomechanical coupling, time dependency, and the von Karman-type geometric non-linearity. Numerical results of the linear third-order theory and non-linear first-order theory are presented to show the effect of the material distribution on the deflections and stresses. Copyright © 2000 John Wiley & Sons, Ltd.
1,460 citations
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: In this paper, the dynamic thermoelastic response of functionally graded cylinders and plates is studied, and a finite element model of the formulation is developed, where the heat conduction and the thermo-elastic equations are solved for a functionally graded axisymmetric cylinder subjected to thermal loading.
Abstract: The dynamic thermoelastic response of functionally graded cylinders and plates is studied. Thermomechanical coupling is included in the formulation, and a finite element model of the formulation is developed. The heat conduction and the thermoelastic equations are solved for a functionally graded axisymmetric cylinder subjected to thermal loading. In addition, a thermoelastic boundary value problem using the first-order shear deformation plate theory (FSDT) that accounts for the transverse shear strains and the rotations, coupled with a three-dimensional heat conduction equation, is formulated for a functionally graded plate. Both problems are studied by varying the volume fraction of a ceramic and a metal using a power law distribution.
1,196 citations
TL;DR: In this article, the limitations of classical laminated plate theory are investigated by comparing solutions of several specific boundary value problems in this theory to the corresponding theory of elasticity solutions, and it is shown that conventional plate theory leads to a very poor description of laminate response at low span-to-depth ratios.
Abstract: Limitations of classical laminated plate theory are investigated by comparing solutions of several specific boundary value problems in this theory to the corresponding theory of elasticity solutions. The general class of problems treated involves the geometric configuration of any number of isotropic or orthotropic layers bonded together and subjected to cylindrical bending. In general it is found that conventional plate theory leads to a very poor description of laminate response at low span-to-depth ratios, but converges to the exact solution as this ratio increases. The analysis presented is also valid in the study of sandwich plates under cylindrical bending.
1,194 citations