Showing papers in "Archives of Computational Methods in Engineering in 2003"

Theories and Finite Elements for Multilayered Plates and Shells:A Unified compact formulation with numerical assessment and benchmarking

Abstract: This work is a sequel of a previous author’s article: “Theories and Finite Elements for Multilayered. Anisotropic, Composite Plates and Shell”, Archive of Computational Methods in Engineering Vol 9, no 2, 2002; in which a literature overview of available modelings for layered flat and curved structures was given. The two following topics, which were not addressed in the previous work, are detailed in this review: 1. derivation of governing equations and finite element matrices for some of the most relevant plate/shell theories; 2. to present an extensive numerical evaluations of available results, along with assessment and benchmarking. The article content has been divided into four parts. An introduction to this review content is given in Part I. A unified description of several modelings based on displacements and transverse stress assumptions ins given in Part II. The order of the expansion in the thickness directions has been taken as a free parameter. Two-dimensional modelings which include Zig-Zag effects, Interlaminar Continuity as well as Layer-Wise (LW), and Equivalent Single Layer (ESL) description have been addressed. Part III quotes governing equations and FE matrices which have been written in a unified manner by making an extensive use of arrays notations. Governing differential equations of double curved shells and finite element matrices of multilayered plates are considered. Principle of Virtual Displacement (PVD) and Reissner’s Mixed Variational Theorem (RMVT), have been employed as statements to drive variationally consistent conditions, e.g.C 0 -Requirements, on the assumed displacements and stransverse stress fields. The number of the nodes in the element has been taken as a free parameter. As a results both differential governing equations and finite element matrices have been written in terms of a few 3×3 fundamental nuclei which have 9 only terms each. A vast and detailed numerical investigation has been given in Part IV. Performances of available theories and finite elements have been compared by building about 40 tables and 16 figures. More than fifty available theories and finite elements have been compared to those developed in the framework of the unified notation discussed in Parts II and III. Closed form solutions and and finite element results related to bending and vibration of plates and shells have been addressed. Zig-zag effects and interlaminar continuity have been evaluated for a number of problems. Different possibilities to get transverse normal stresses have been compared. LW results have been systematically compared to ESL ones. Detailed evaluations of transverse normal stress effects are given. Exhaustive assessment has been conducted in the Tables 28–39 which compare more than 40 models to evaluate local and global response of layered structures. A final Meyer-Piening problem is used to asses two-dimensional modelings vs local effects description.

Overview and recent advances in natural neighbour galerkin methods

Abstract: In this paper, a survey of the most relevant advances in natural neighbour Galerkin methods is presented. In these methods (also known as natural element methods, NEM), the Sibson and the Laplace (non-Sibsonian) interpolation schemes are used as trial and test functions in a Galerkin procedure. Natural neighbour-based methods have certain unique features among the wide family of so-called meshless methods: a well-defined and robust approximation with no user-defined parameters on non-uniform grids, and the ability to exactly impose essential (Dirichlet) boundary conditions are particularly noteworthy. A comprehensive review of the method is conducted, including a description of the Sibson and the Laplace interpolants in two- and three-dimensions. Application of the NEM to linear and non-linear problems in solid as well as fluid mechanics is studied. Other issues that are pertinent to the vast majority of meshless methods, such as numerical quadrature, imposing essential boundary conditions, and the handling of secondary variables are also addressed. The paper is concluded with some benchmark computations that demonstrate the accuracy and the key advantages of this numerical method.

Computational developments for simulation based design: Multi-scale physics and flow/thermal/cure/stress modeling, analysis, and validation for advanced manufacturing of composites with complex microstructures

Abstract: In the process modeling and manufacturing of large geometrically complex lightweight structural components comprising of fiber-reinforced composite materials with complex microstructures by Resin Transfer Molding (RTM), a polymer resin is injected into a mold cavity filled with porous fibrous preforms. The over-all success of the manufacturing process depends on the complete impregnation of the fiber preform by the polymer resin, prevention of polymer gelation during filling, and subsequent avoidance of dry spots. Since the RTM process involves the injection of a cold resin into a heated mold, the associated multi-physics encompasses a moving boundary value problem in conjunction with the multi-disciplinary and multi-scale study of flow/thermal/cure and the subsequent prediction of residual stresses in side the mold cavity. Although experimental validations are indispensable, routine manufacture of large complex structural geometries can only be enhanced via computational simulations; thus, eliminating costly trial runs and helping designers in the set-up of the manufacturing process. This manuscript describes an in-depth study of the mathematical and computational developments towards formulating an effective simulation-based design methodology using the finite element method. The present methodology is well suited for applications to practical engineering structural components encountered in the manufacture of complex RTM type lightweight composites, and encompasses both thick and thin shell-type composites with the following distinguishing features: (i) an implicit pure finite element computational methodology to track the fluid flow fronts with illustrations first to isothermal situations to overcome the deficiencies of traditional explicit type methods while permitting standard mesh generators to be employed in a straightforward manner: (ii) a methodology for predicting the effective constitutive model thermophysical properties, namely, the permeability tensor of the fiber preform microstructures in both virgin and manufactured states, the conductivity tensor, and the elasticity tensor; (iii) extension of the implicit pure finite element methodology to non-isothermal situations with and without influence of thermal dispersion to accurately capture the physics of the RTM process; (iv) stabilizing features to reduce oscillatory solution behavior typically encountered in the numerical analysis of these classes of problems: and (v) as a first step, preliminary investigations towards the prediction of residual stresses induced in the manufacturing process during post-cure cool-down. The underlying theory and formulations detailing the relevant volume averaging and homogenization techniques are first outlined for the multi-scale problem. Then the implicit pure finite element methodology, followed by the models for permeability prediction, is presented and compared for the case of isothermal mold filling. Applications of the pure finite element method is next extended to non-isothermal situations to accurately capture the flow/thermal/cure effects and the physics of the RTM process. Subsequently, a preliminary attempt is made to integrate the developments with the problem of thermoelasticity for residual stress prediction during post-cure cool-down. Where applicable, extensive validations of numerical results are made with analytical solutions and/or available experimental data. From these comparisons, relevant conclusions are drawn about the effectiveness of the present developments and their subsequent application to large-scale practical analysis of fiber-reinforced composite structures. Finally, some future directions relevant to the present study encompassing the multi-physics and multi-scale aspects of fibrous preforms with complex microstructures for use in lightweight composites are outlined.