J. N. Reddy's Introduction to the Finite Element Method PDF

By J. N. Reddy

ISBN-10: 0070513554

ISBN-13: 9780070513556

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Extra resources for Introduction to the Finite Element Method

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2. , large gradients of the solution). The three fundamental steps of the finite element method that are illustrated via the examples are: 1. Divide the whole into parts (both to represent the geometry and solution of the problem). 2. Over each part, seek an approximation to the solution as a linear combination of nodal values and approximation functions. 3. Derive the algebraic relations among the nodal values of the solution over each part, and assemble the parts to obtain the solution to the whole.

The collection of finite elements is called the finite element mesh. 2. Over each finite element, the physical process is approximated by functions of desired type (polynomials or otherwise), and algebraic equations relating physical quantities at selective points, called nodes, of the element are developed. 3. The element equations are assembled using continuity and/or "balance" of physical quantities. In the finite element method, in general, we seek an approximate solution u to a differential equation in the form n U = L j=l m Uj1J1j + 2: Cj4Jj j=l 16 PRELIMINARIES u where Uj are the values of at the element nodes, 1jJ; are the interpolation functions, Cj are the nodeless coefficients, and

22b)], we obtain 0= 1[ (- - + - Q k aWaT ax ax awa;) -wqo] dxdyBy ay f r aT) ds wk (aT -n... e. 22)]. From the boundary expression, it follows that the secondary variable of the problem is of the form k( aT n + aT n ) ax:< ay = k aT == q Y an " and the primary variable is T. , along the normal to) the boundary. In general, q" is composed of fluxes due to conduction, convection, and radiation. The boundary r of the domain consists of several line segments, and they are subject to different types of boundary conditions (see Fig.

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Introduction to the Finite Element Method by J. N. Reddy


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