Introduction to ABAQUS Appendix 1 Introduction to Finite Element Analysis Copyright 2004 ABAQUS, Inc. Introduction to ABAQUS Overview • What are Finite Elements? • Objectives of Finite Element Analysis • Components of an Analysis Model Copyright 2004 ABAQUS, Inc. A1.2 Introduction to ABAQUS What are Finite Elements? Copyright 2004 ABAQUS, Inc. Introduction to ABAQUS A1.4 What are Finite Elements? • In the finite element method a domain is subdivided and modeled as an assembly of discrete regions called finite elements. finite element discretization of ¼ of the plate the domain is a plate with a hole Copyright 2004 ABAQUS, Inc. Introduction to ABAQUS A1.5 What are Finite Elements? • The shape of the solution field (e.g., displacement, temperature, etc.) in each element is approximated. – Polynomial functions are commonly used. – Only the magnitude of the solution field needs to be determined. (Figure based on image from Numerical Solution of Partial Differential Equations by the Finite Element Method by C. Johnson.) Copyright 2004 ABAQUS, Inc. Introduction to ABAQUS A1.6 What are Finite Elements? • All the elements comprising the domain are assembled and the resulting matrix equations are solved such that: – The solution is continuous across element boundaries. – Equilibrium is achieved, and the prescribed boundary conditions are satisfied. Copyright 2004 ABAQUS, Inc. Introduction to ABAQUS Objectives of Finite Element Analysis Copyright 2004 ABAQUS, Inc. Introduction to ABAQUS A1.8 Objectives of Finite Element Analysis • The primary objective of any finite element analysis (FEA) is to numerically simulate the response of a structure (the response may be structural, thermal, acoustic, etc.) to a given set of conditions for the purpose of: – Design • Reduce product development cycle • Reduce tooling costs • Improve product quality – Assessing existing structures • Analyze damage in a part • Loading not envisioned during design – Establishing the causes of failure in a structure – Research • Material model development – Etc. Copyright 2004 ABAQUS, Inc. Introduction to ABAQUS Components of an Analysis Model Copyright 2004 ABAQUS, Inc. Introduction to ABAQUS A1.10 Components of an Analysis Model • There are five major components of any finite element model: – Geometry – Properties – Analysis history – Output – Loads and boundary conditions • Together these components describe the physical problem to be analyzed and the results to be obtained. Copyright 2004 ABAQUS, Inc. Introduction to ABAQUS A1.11 Components of an Analysis Model • Geometry – We distinguish between physical geometry and discrete geometry. • The physical geometry describes the actual geometry of a structure. • The discrete geometry is an approximation of the physical geometry. – It consists of nodes and elements. physical gear geometry Copyright 2004 ABAQUS, Inc. discrete gear geometry Introduction to ABAQUS A1.12 Components of an Analysis Model • Properties – The model properties include the material properties and properties that complete geometry descriptions (these are called section properties in ABAQUS). shell thickness: 1 mm shell thickness: 3 mm Material properties Copyright 2004 ABAQUS, Inc. Section properties Introduction to ABAQUS A1.13 Components of an Analysis Model • Analysis history – The analysis attempts to simulate a history of events. This history is generally divided into a series of analysis steps. • An analysis procedure is associated with each step. – The analysis procedure describes the type of response sought in the step. • The response may be: – Structural (quasi-static or dynamic behavior) – Nonstructural (thermal, acoustic, etc.) • Coupling between different fields may be important (e.g., thermalmechanical, structural-acoustic, thermal-electrical, etc.) • The time-dependent (transient) or long-term (steady-state) response may be investigated. Copyright 2004 ABAQUS, Inc. Introduction to ABAQUS Components of an Analysis Model • Example: Manufacture and use of a sink. Copyright 2004 ABAQUS, Inc. A1.14 Introduction to ABAQUS A1.15 Components of an Analysis Model • Output – Finite element models can generate vast amounts of output. – You should decide what output is of interest before submitting a model for analysis. • This will make it easier to examine the results and to allow more efficient use of available computer resources. – In ABAQUS several types of output are available, including field and history output. Copyright 2004 ABAQUS, Inc. Introduction to ABAQUS A1.16 Components of an Analysis Model – Field output allows you to get a global sense of the response. • The output is requested for large regions of the model (usually all) but is generally written a limited number times during the course of the simulation. Example: Field output is used to create deformed shape and contour plots. (Courtesy of ABB Turbo Systems Ltd.) Copyright 2004 ABAQUS, Inc. Introduction to ABAQUS A1.17 Components of an Analysis Model – History output allows you to get a detailed understanding of the response in an isolated region of the model. • The output is restricted to selected regions of the model but is generally written very frequently during the course of the simulation. Example: History output is used to create X–Y plots. Copyright 2004 ABAQUS, Inc. Introduction to ABAQUS A1.18 Components of an Analysis Model • Loads and boundary conditions – In general, a load refers to anything that induces a change in the state of a structure from its initial state. These include fluxes and boundary conditions. – Fluxes • Concentrated forces, distributed pressures, heat fluxes, etc. P concentrated force Copyright 2004 ABAQUS, Inc. p pressure load or distributed heat flux Introduction to ABAQUS A1.19 Components of an Analysis Model • Boundary conditions – Values of the solution field that are prescribed, such as prescribed displacements and temperatures. – The values may be zero (fixed) or nonzero. nonzero translations or velocities fixed translations and rotations Copyright 2004 ABAQUS, Inc. u or v
