An Improved Reissner-Mindlin Plate Theory for Composite Laminates

Aerospace ◽  
2004 ◽  
Author(s):  
Wenbin Yu
Keyword(s):  
Exact Solution ◽  
Asymptotic Method ◽  
Composite Laminates ◽  
Plate Theory ◽  
Three Dimensional ◽  
Mindlin Plate ◽  
Two Dimensional ◽  
Previous Theory ◽  
Variational Asymptotic ◽  
Variational Asymptotic Method

An improved Reissner-Mindlin theory for composite laminates without invoking ad hoc kinematic assumptions is constructed using the variational-asymptotic method. Instead of assuming a priori the distribution of three-dimensional displacements in terms of two-dimensional plate displacements as what is usually done in typical plate theories, an exact intrinsic formulation has been achieved by introducing unknown three-dimensional warping functions. Then the variational-asymptotic method is applied to systematically decouple the original three-dimensional problem into a one-dimensional through-the-thickness analysis and a two-dimensional plate analysis. The resulting theory is an equivalent single-layer Reissner-Mindlin theory with an excellent accuracy comparable to that of higher-order, layerwise theories. The present work is extended from the previous theory developed by the writer and his co-workers with two sizable contributions: (a) six more constants (33 in total) are introduced to allow maximum freedom to transform the asymptotically correct energy into a Reissner-Mindlin model; and (b) the semi-definite programming technique is used to seek the optimum Reissner-Mindlin model. Furthermore, it is proved the first time that the recovered three-dimensional quantities exactly satisfy the continuity conditions on the interface between different layers and traction boundary conditions on the bottom and top surfaces. It is also shown that that two of the equilibrium equations of three-dimensional elasticity can be satisfied asymptotically, and the third one can be satisfied approximately so that the difference between the Reissner-Mindlin model and the second order asymptotical energy can be minimized. Numerical examples are presented to compare with the exact solution as well as the classical lamination theory and first-order shear-deformation, demonstrating that the present theory has an excellent agreement with the exact solution.

Derivation of Plate Theory Accounting Asymptotically Correct Shear Deformation

1997 ◽  
Vol 64 (4) ◽  
pp. 905-915 ◽  
Author(s):  
V. G. Sutyrin
Keyword(s):  
Shear Deformation ◽  
Asymptotic Method ◽  
Plate Theory ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Optimization Procedure ◽  
Laminated Plates ◽  
Orthotropic Plates ◽  
Variational Asymptotic ◽  
Variational Asymptotic Method

The focus of this paper is the development of linear, asymptotically correct theories for inhomogeneous orthotropic plates, for example, laminated plates with orthotropic laminae. It is noted that the method used can be easily extended to develop nonlinear theories for plates with generally anisotropic inhomogeneity. The development, based on variational-asymptotic method, begins with three-dimensional elasticity and mathematically splits the analysis into two separate problems: a one-dimensional through-the-thickness analysis and a two-dimensional “plate” analysis. The through-the-thickness analysis provides elastic constants for use in the plate theory and approximate closed-form recovering relations for all truly three-dimensional displacements, stresses, and strains expressed in terms of plate variables. In general, the specific type of plate theory that results from variational-asymptotic method is determined by the method itself. However, the procedure does not determine the plate theory uniquely, and one may use the freedom appeared to simplify the plate theory as much as possible. The simplest and the most suitable for engineering purposes plate theory would be a “Reissner-like” plate theory, also called first-order shear deformation theory. However, it is shown that construction of an asymptotically correct Reissner-like theory for laminated plates is not possible in general. A new point of view on the variational-asymptotic method is presented, leading to an optimization procedure that permits a derived theory to be as close to asymptotical correctness as possible while it is a Reissner-like. This uniquely determines the plate theory. Numerical results from such an optimum Reissner-like theory are presented. These results include comparisons of plate displacement as well as of three-dimensional field variables and are the best of all extant Reissner-like theories. Indeed, they even surpass results from theories that carry many more generalized displacement variables. Although the derivation presented herein is inspired by, and completely equivalent to, the well-known variational-asymptotic method, the new procedure looks different. In fact, one does not have to be familiar with the variational-asymptotic method in order to follow the present derivation.

Prediction of Mechanical Properties of Microcellular Plastics Using the Variational Asymptotic Method for Unit Cell Homogenization (VAMUCH) Method

2013 ◽  
Author(s):  
Emily Yu ◽  
Lih-Sheng Turng
Keyword(s):  
Mechanical Properties ◽  
Asymptotic Method ◽  
Thermoplastic Polyurethane ◽  
Three Dimensional ◽  
Unit Cell ◽  
Element Analysis ◽  
Microcellular Plastics ◽  
Variational Asymptotic ◽  
Variational Asymptotic Method ◽  
Injection Molded

This work presents the application of the micromechanical variational asymptotic method for unit cell homogenization (VAMUCH) with a three-dimensional unit cell (UC) structure and a coupled, macroscale finite element analysis for analyzing and predicting the effective elastic properties of microcellular injection molded plastics. A series of injection molded plastic samples — which included polylactic acid (PLA), polypropylene (PP), polystyrene (PS), and thermoplastic polyurethane (TPU) — with microcellular foamed structures were produced and their mechanical properties were compared with predicted values. The results showed that for most material samples, the numerical prediction was in fairly good agreement with experimental results, which demonstrates the applicability and reliability of VAMUCH in analyzing the mechanical properties of porous materials. The study also found that material characteristics such as brittleness or ductility could influence the predicted results and that the VAMUCH prediction could be improved when the UC structure was more representative of the real composition.

Asymptotic theory of 3D thermoelastic stress analysis of honeycomb sandwich panels with composite facesheets

2018 ◽  
Vol 22 (6) ◽  
pp. 1952-1982
Author(s):  
MV Peereswara Rao ◽  
K Renji ◽  
Dineshkumar Harursampath
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Present Theory ◽  
Two Dimensional ◽  
Composite Sandwich ◽  
Variational Asymptotic ◽  
Small Parameters ◽  
Dimensional Finite Element ◽  
Variational Asymptotic Method ◽  
Three Dimensional Finite Element

This work presents an asymptotical thermoelastic model for analyzing symmetric composite sandwich plate structures. Use of three-dimensional finite elements to analyze real-life composite sandwich structures is computationally prohibitive, while use of two-dimensional finite element cannot accurately predict the transverse stresses and three-dimensional displacements. Endeavoring to fill this gap, the present theory is developed based on the variational asymptotic method. The unique features of this work are the identification and utilization of small parameters characterizing the geometry and material stiffness coefficients of sandwich structural panels in addition to the small parameters pertaining to any plate-like structure. In this formulation, using variational asymptotic method, the three-dimensional thermoelastic problem is mathematically split into a one-dimensional through-the-thickness analysis, and a two-dimensional reference surface analysis. The through-the-thickness analysis provides the constitutive relation between the generalized two-dimensional strains, and the generalized force resultants for the plate analysis, it also provides a set of closed-form solutions to express the three-dimensional responses in terms of two-dimensional variables, which are determined by solving the equilibrium equations of the plate reference surface. Numerical results are illustrated for a typical composite sandwich panel subjected to a linear-bisinusoidal thermal loading. The three-dimensional responses of the composite sandwich structure from the present theory are compared with the three-dimensional finite element solutions of MSC NASTRAN®. The results from the present theory agree closely with three-dimensional finite element results and yet enable order of magnitude saving in computational resources and time.

scholarly journals Parametric structural modelling of fish bone active camber morphing aerofoils

2018 ◽  
Vol 29 (9) ◽  
pp. 2008-2026 ◽  
Author(s):  
Andres E Rivero ◽  
Paul M Weaver ◽  
Jonathan E Cooper ◽  
Benjamin KS Woods
Keyword(s):  
Analytical Model ◽  
Composite Laminates ◽  
Plate Theory ◽  
Ritz Method ◽  
Linear Equations ◽  
Variable Stiffness ◽  
Automated Analysis ◽  
Fish Bone ◽  
Two Dimensional ◽  
Wide Range

Camber morphing aerofoils have the potential to significantly improve the efficiency of fixed and rotary wing aircraft by providing significant lift control authority to a wing, at a lower drag penalty than traditional plain flaps. A rapid, mesh-independent and two-dimensional analytical model of the fish bone active camber concept is presented. Existing structural models of this concept are one-dimensional and isotropic and therefore unable to capture either material anisotropy or spanwise variations in loading/deformation. The proposed model addresses these shortcomings by being able to analyse composite laminates and solve for static two-dimensional displacement fields. Kirchhoff–Love plate theory, along with the Rayleigh–Ritz method, are used to capture the complex and variable stiffness nature of the fish bone active camber concept in a single system of linear equations. Results show errors between 0.5% and 8% for static deflections under representative uniform pressure loadings and applied actuation moments (except when transverse shear exists), compared to finite element method. The robustness, mesh-independence and analytical nature of this model, combined with a modular, parameter-driven geometry definition, facilitate a fast and automated analysis of a wide range of fish bone active camber concept configurations. This analytical model is therefore a powerful tool for use in trade studies, fluid–structure interaction and design optimisation.

scholarly journals Geometric Nonlinear Analysis of Composite Stiffened Panels Using Variational Asymptotic Method

AIAA Journal ◽  
2020 ◽  
Vol 58 (9) ◽  
pp. 4189-4203
Author(s):  
K. Jagath Narayana ◽  
Ramesh Gupta Burela ◽  
Sathiskumar Anusuya Ponnusami ◽  
Dineshkumar Harursampath
Keyword(s):  
Nonlinear Analysis ◽  
Asymptotic Method ◽  
Stiffened Panels ◽  
Geometric Nonlinear ◽  
Variational Asymptotic ◽  
Variational Asymptotic Method ◽  
Geometric Nonlinear Analysis
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