Elemntos Finitos

T. Belytschko, Introduction, December 16, 1998

CHAPTER 1 INTRODUCTION
by Ted Belytschko Northwestern University Copyright 1996 1.1 NONLINEAR FINITE ELEMENTS IN DESIGN Nonlinear finite element analysis is an essential component of computeraided design. Testing of prototypes is increasingly being replaced by simulation with nonlinear finite element methods because this provides a morerapid and less expensive way to evaluate design concepts and design details. For example, in the field of automotive design, simulation of crashes is replacing full scale tests, both for the evaluation of early design concepts and details of the final design, such as accelerometer placement for airbag deployment, padding of the interior, and selection of materials and component cross-sections formeeting crashworthiness criteria. In many fields of manufacturing, simulation is speeding the design process by allowing simulation of processes such as sheet-metal forming, extrusion of parts, and casting. In the electronics industries, simulation is replacing drop-tests for the evaluation of product durability. For both users and developers of nonlinear finite element programs, an understanding ofthe fundamental concepts of nonlinear finite element analysis is essential. Without an understanding of the fundamentals, a user must treat the finite element program as a black box that provides simulations. However, even more so than linear finite element analysis, nonlinear finite element analysis confronts the user with many choices and pitfalls. Without an understanding of the implication andmeaning of these choices and difficulties, a user is at a severe disadvantage. The purpose of this book is to describe the methods of nonlinear finite element analysis for solid mechanics. Our intent is to provide an integrated treatment so that the reader can gain an understanding of the fundamental methods, a feeling for the comparative usefulness of different approaches and an appreciation ofthe difficulties which lurk in the nonlinear world. At the same time, enough detail about the implementation of various techniques is given so that they can be programmed. Nonlinear analysis consists of the following steps: 1. development of a model; 2. formulation of the governing equations; 3. discretization of the equations; 4. solution of the equations;

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T. Belytschko, Introduction,December 16, 1998 5. interpretation of the results. Modeling is a term that tends to be used for two distinct tasks in engineering. The older definition emphasizes the extraction of the essential elements of mechanical behavior. The objective in this approach is to identify the simplest model which can replicate the behavior of interest. In this approach, model development is the process ofidentifying the ingredients of the model which can provide the qualitative and quantitative predictions. A second approach to modeling, which is becoming more common in industry, is to develop a detailed, single model of a design and to use it to examine all of the engineering criteria which are of interest. The impetus for this approach to modeling is that it costs far more to make a model or mesh foran engineering product than can be saved through reduction of the model by specializing it for each application. For example, the same finite element model of a laptop computer can be used for a drop-test simulation, a linear static analysis and a thermal analysis. By using the same model for all of these analyses, a significant amount of engineering time can be saved. While this approach is notrecommended in all situations, it is becoming commonplace in industry. In the near future the finite element model may serve as a prototype that can be used for checking many aspects of a design’s performance. The decreasing cost of computer time and the increasing speed of computers make this approach highly cost-effective. However the user of finite element software must still able to evaluate...