fe研發(fā)培訓(xùn),設(shè)計(jì)培訓(xùn)(存儲版)
【正文】 nction defined over a domain can be approximated by a discrete model posed of a set of piecewise continuous functions defined over a finite number of subdomains. Fundamental Concept ? Consider an example of temperature distribution in a bar. Fundamental Concept ? The continuous function is T(x) and the domain is OL along xaxis.? Six points along xaxis are identified. We shall call these points as nodes.? The domain is divided into five elements.? Function T(x) is approximated by five piecewise continuous linear functions defined over a single element. Fundamental Concept ? The preprocessing includes the steps of identifying the domain of analysis, derivation of the governing and boundary equations and the division of the domain into subdomains called finite elements. Preprocessing? Consider onedimensional bar element. ? The value of a function over the element i is defined Preprocessing ? Similarly, for element j Preprocessing ?The most mon twodimensional element is a triangle. Preprocessing Preprocessing? The governing equation for 2D magic field problem can be derived from Maxwell’s equations by defining a potential function A. ?A residual is defined for an approximate solution. Preprocessing? Minimizing the weighted residual with respect to each nodal potential, we obtain ? Substituting from above, we obtain. Preprocessing? Using Green’s identity, we obtain. ?Substituting, we obtain the following equations. Preprocessing? In the processing step, we solve the system of equations derived in the preprocessing step. Processing? The coefficient matrix for the system of equations is sparse and is usually symmetrical along the diagonal.? For nonlinear magic field problems, the entries in the coefficient matrix are functions of permeability.? An iterative method, such as, NewtonRaphson is used for solution of the nonlinear system of equations. Processing? The princip
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