Three-Dimensional Plate Theory for Flexible Multibody Dynamics

2015 ◽  
Author(s):  
Shilei Han ◽  
Olivier A. Bauchau
Keyword(s):  
Plate Theory ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Flexible Multibody Dynamics ◽  
Composite Plates ◽  
Complex Stress ◽  
Mindlin Plate ◽  
Stress States ◽  
Three Dimensional Elasticity ◽  
Material Line

In structural analysis, many components are approximated as plates. More often that not, classical plate theories, such as Kirchhoff or Reissner-Mindlin plate theories, form the basis of the analytical developments. The advantage of these approaches is that they leads to simple kinematic descriptions of the problem: the plate’s normal material line is assumed to remain straight and its displacement field is fully defined by three displacement and two rotation components. While such approach is capable of capturing the kinetic energy of the system accurately, it cannot represent the strain energy adequately. For instance, it is well known from three-dimensional elasticity theory that the normal material line will warp under load for laminated composite plates, leading to three-dimensional deformations that generate complex stress states. To overcome this problem, several high-order, refined plate theories have been proposed. While these approaches work well for some cases, they often lead to inefficient formulations because they introduce numerous additional variables. This paper presents a different approach to the problem: based on a finite element semi-discretization of the normal material line, plate equations are derived from three-dimensional elasticity using a rigorous dimensional reduction procedure.

Advanced Plate Theory for Multibody Dynamics

2013 ◽  
Author(s):  
Olivier A. Bauchau ◽  
Shilei Han
Keyword(s):  
Plate Theory ◽  
Three Dimensional ◽  
Hamiltonian Formalism ◽  
Laminated Composite ◽  
Composite Plates ◽  
Complex Stress State ◽  
Mindlin Plate ◽  
Element Discretization ◽  
Deformation State ◽  
Material Line

In flexible multibody systems, many components are often approximated as plates. More often that not, classical plate theories, such as Kirchhoff or Reissner-Mindlin plate theory, form the basis of the analytical development for plate dynamics. The advantage of this approach is that it leads to a very simple kinematic representation of the problem: the plate’s normal material line is assumed to remain straight and its displacement field is fully defined by three displacement and two rotation components. While such approach is capable of capturing the kinetic energy of the system accurately, it cannot represent the strain energy adequately. For instance, it is well known from three-dimensional elasticity theory that the normal material line will warp under load for laminated composite plates, leading to a three-dimensional deformation state that generates a complex stress state. To overcome this problem, several high-order and refined plate theory were proposed. While these approaches work well for some cases, they typically lead to inefficient formulation because they introduce numerous additional variables. This paper presents a different approach to the problem, which is based on a finite element discretization of the normal material line, and relies of the Hamiltonian formalism of obtain solutions of the governing equations. Polynomial solutions, also known as central solutions, are obtained that propagate over the entire span of the plate.

A JUSTIFICATION OF THE REISSNER–MINDLIN PLATE THEORY THROUGH VARIATIONAL CONVERGENCE

2007 ◽  
Vol 05 (02) ◽  
pp. 165-182 ◽  
Author(s):  
ROBERTO PARONI ◽  
PAOLO PODIO-GUIDUGLI ◽  
GIUSEPPE TOMASSETTI
Keyword(s):  
Plate Theory ◽  
Scaling Law ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Energy Functional ◽  
Mindlin Plate ◽  
Variational Convergence ◽  
Mindlin Plate Theory ◽  
Γ Convergence ◽  
Three Dimensional Elasticity

We provide a justification of the Reissner–Mindlin plate theory, using linear three-dimensional elasticity as framework and Γ-convergence as technical tool. Essential to our developments is the selection of a transversely isotropic material class whose stored energy depends on (first and) second gradients of the displacement field. Our choices of a candidate Γ-limit and a scaling law of the basic energy functional in terms of a thinness parameter are guided by mechanical and formal arguments that our variational convergence theorem is meant to validate mathematically.

A Variational Approach to Three-Dimensional Elasticity Solutions of Laminated Composite Plates

1992 ◽  
Vol 59 (2S) ◽  
pp. S166-S175 ◽  
Author(s):  
M. Savoia ◽  
J. N. Reddy
Keyword(s):  
Composite Laminates ◽  
Separation Of Variables ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Composite Plates ◽  
Approximate Solutions ◽  
Transverse Load ◽  
Rectangular Plates ◽  
Elasticity Solutions ◽  
Three Dimensional Elasticity

The displacements in a laminated composite are represented as products of two sets of unknown functions, one of which is only a function of the thickness coordinate and the other is a function of the in-plane coordinates (i.e., separation of variables approach), and the minimization of the total potential energy is reduced to a sequence of iterative linear problems. Analytical solutions are developed for cross-ply and angle-ply laminated composite rectangular plates. The solution for simply-supported cross-ply plates under sinusoidal transverse load reduces to that of Pagano. Numerical results for stresses and displacements for antisymmetric angle-ply laminates are presented. The three-dimensional elasticity solutions developed are important because they can be used to study the behavior of composite laminates, in addition to serving as reference for approximate solutions by numerical methods and twodimensional theories.

Hygrothermal Buckling Response of Laminated Composite Plates with Random Material Properties: Micro-Mechanical Model

2011 ◽  
Vol 110-116 ◽  
pp. 113-119 ◽  
Author(s):  
Rajesh Kumar ◽  
Dharamveer Singh
Keyword(s):  
Material Properties ◽  
Plate Theory ◽  
Perturbation Technique ◽  
Micromechanical Model ◽  
Laminated Composite ◽  
Composite Plates ◽  
Second Order Statistics ◽  
Operational Life ◽  
Safety And Reliability ◽  
Random Material Properties

The aim of this paper is to find out the randomness in the material properties on the buckling of laminated composite plate needed for the economy, safety and reliability of the structures and components in their operational life especially for sensitive Aerospace Engineering applications in hygrothermal environments. Micromechanical model has been taken for the analysis .The used methodology is a C0 finite element method based on higher-order shear deformation plate theory for deriving the standard eigenvalue problem. A Taylor series based mean-centered first order perturbation technique is used to find out the second order statistics of the hygrothermal buckling loads under different sets of environmental conditions..The numerical results for deterministic parameters are compared and validated with available literature and random parameters with independent Monte Carlo Simulation. The result shows that the plate is significantly affected by the hygrothermal buckling load.

Analysis of Symmetric Angle-Ply Laminated Composite Skew Plates Using Hybrid Trefftz Finite Element

2019 ◽  
Author(s):  
Subhasankar Dwibedi
Keyword(s):  
Finite Element ◽  
Composite Structures ◽  
Plate Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Point Load ◽  
Shear Stresses ◽  
Skew Angle ◽  
Distributed Load ◽  
Trefftz Finite Element

Abstract Analysis of symmetric angle-ply skew laminated composite plates has been presented in the study using a newly developed hybrid Trefftz finite element (hTFE). Mindlin’s plate theory has been used to develop the present hTFE. The forms of displacement are assumed such that governing partial differential equations are satisfied a priori inside the element domain. Particular solutions of the governing equations have been ignored and Trefftz functions are derived using the homogenous solutions only. Inter-element continuity has been established by employing another displacement field along the edges of the hTFEs. The transverse shear stresses have been ignored at the top and bottom surfaces of the laminate. The angle of inclination of the width of the plate with the y-axis has been taken as the skew angle and different forms of skew plates are obtained by varying the skew angle. Sinusoidally distributed load (SDL), uniformly distributed load (UDL), and point load (PL) have been subjected to the top surface of the laminate and the non-dimensionalized center point deflection have been evaluated to assess the performance of the present hTFE. The observation from the present study further reinforce the versatility of the hTFE method for analysis of composite structures with complex shapes or geometries.

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