Textbook of Finite Element Analysis - download pdf or read online

By P. Seshu

ISBN-10: 8120323157

ISBN-13: 9788120323155

Designed for a one semester path in finite point procedure, this compact and good equipped textual content offers FEM as a device to discover approximate suggestions to differential equations.

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Extra info for Textbook of Finite Element Analysis

Example text

6 shows a plot of the domain residual in each case. In this way, we are able to generate different approximate solutions to the problem but each of these solutions deviates appreciably from the exact solution. We can improve our trial solution by adding one more term to the Sine series. 8 –-11 Fig. 4). 29) Since we have two constants to be determined, we can set the residual zero at two selected points. 7 compares the solution vˆ (x) obtained in this manner against the classical exact solution.

From the boundary conditions that vˆ (0) = 0 and d vˆ /dx (0) = 0, we have c0 = 0 = c1. 19) We thus observe that finding trial solution functions that satisfy all the boundary conditions could, in general, be cumbersome. Step 2: Find the domain residual. 20) Step 3: Minimise the residual. 21) vˆ (x) = q0/(24EI) [x4 – 4Lx3 + 6x2L2] which can be readily verified to be the exact solution itself. This is to be expected since we were able to make the residual identically zero within the entire domain.

Evaluate the sub-domain level contributions to the weighted residual by merely computing the integral ò Wi(x)Rd(x) dx or its weak form, just once for the kth subdomain. Ø Build up the entire coefficient matrices [A] and {b} by appropriately placing these subdomain level contributions in the appropriate rows and columns. , function values fk at the ends of the sub-domains. Once the function values fk at the ends of the sub-domains have been determined in this manner, the value of the function at any interior point can be obtained using the appropriate interpolation functions.

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Textbook of Finite Element Analysis by P. Seshu

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