AutoFEM Analysis is a finite element analysis software.
The main feature of the system is its deep integration with AutoCAD
By using AutoFEM Analysis an user of AutoCAD gets possibility solve the problem of finite-element modeling of various physical phenomena:
General algorithm of working with AutoFEM Analysis is the following:
First, the user should create three-dimensional (3D) model of the product in the AutoCAD 3D environment.
Then, without leaving AutoCAD, the user creates a problem of finite element analysis so called as a «Study».
The model is loaded into the Preprocessor of AutoFEM Analysis which is fully integrated into AutoCAD.
By using the Preprocessor the user specifies the external and internal parameters of the simulated physical phenomena (finite element mesh, boundary conditions, materials, etc.) and transmits the «Study» in Processor of AutoFEM Analysis.
Processor of AutoFEM Analysis performs assembling and solution of systems of algebraic equations in accordance with the finite element method. In the AutoFEM Analysis Postprocessor the user performs an analysis of the results and the formation of the accompanying documents - reports, video, avi, etc.
Thus users of AutoCAD are able to perform the finite element analysis in the usual and familiar for them software environment.
And there is a FREE finite element analysis software - AutoFEM Analysis Lite - which is available for use to each user of AutoCAD 2007-2010.
Theoretical background of AutoFEM Analysis
AutoFEM Analysis – is a finite element analysis software, based on finite element method.
Finite element method (FEM) is the leading way to predict the behaviour of structures in real-life conditions.
The general principle of the finite element method is as follows.
The design, which is, in general, a system with an infinite number of degrees of freedom, is divided into a finite number of elementary volumes - the so-called finite elements. Since the form of a finite element is known in advance (bar, beam, triangle, wedge, prism etc.) it is possible to write the relations that establish a mathematical relationship between variations of a physical quantity within a single element.
For example, for the problem of static strength analysis is determined the dependence of the geometric shape of a finite element (strain) of the element attached to the external forces. Geometric shape of a finite element is defined by spatial coordinates of specific points on the boundaries of a finite element, which are called nodes. Application to finite element forces causes a shift of nodes (strain). This shift can be expressed in the form of algebraic equations. For the thermal analysis determined the dependence of the temperature distribution in terms of finite element.
For each finite element is constructed a system of algebraic equations describing the mathematical formulation of the physical problem. For example, for the problem of static strength in the matrix form the system of equations can be written as
[Kel] * [Xel] = [Pel], where
[Kel] - stiffness matrix of finite element
[Pel] - vector of forces applied to the finite element
[Xel] - the unknown vector of displacements at characteristic points of the finite element, called nodes. This vector is to be determined.
In the first version AutoFEM Analysis as a finite element used tetrahedron. Tetrahedron can approximate arbitrarily complex geometry of the simulated real object. A special generator of finite element mesh creates a tetrahedral finite element mesh for three-dimensional solid model of a product, made in AutoCAD.
After building the finite element mesh and the computation of local stiffness matrices of each finite element it is possible to algebraically and topologically sum up all the local stiffness matrix elements and to construct the global stiffness matrix of the assembly. The result (for example, stress static analysis) is a system of equations of the form
[KGl] * [XGL] = [PGl], where
[KGl] - global stiffness matrix of construction.
[PGl] - the global vector of external forces.
[XG] - to be determined the vector of unknown nodal displacements.
Processor of AutoFEM Analysis performs the generation of the global stiffness matrix and solution of algebraic equations. There are some methods for solving algebraic equations. One of the most famous and used is Gauss method (or its modifications such as Cholesky method). This methods usually are called as Direct methods of algebraic equations solving. The second big group of linear algebra methods for solving algebraic equations is Iterative methods of algebraic equations solving such as Conjugate gradient method.
Processor of AutoFEM Analysis uses both of these groups methods for solving linear and non-linear algebraic equations which are considered in finite element modelling.
After solving the equations at each node of the finite element mesh is known displacement and stress (for statics), or other physical quantities such as temperature for the thermal analysis. These data are transmitted into Postprocessor of AutoFEM Analysis, which has been fully integrated into the interface of AutoCAD.
The theory of finite element method is described in many books and articles. It is not easy to recommend any of them, because there quantities is about hundred of thousands. Possibly one of the most famous author about FEM theme is O.C. Zienkiewicz. His books have been translated into all European languages. For example, one of the last edition of his book is Zienkiewicz O.C., Taylor R.L. Vol. 1-3. The finite element method. (2000)(T).
AutoFEM Analysis uses various finite element algorithms which are described in scientific articles and special books on FEA and FEM thematics.
Conjugate gradient method
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