An Introduction to The Finite Element Method[Solutions] by J Reddy

By J Reddy

J.N. Reddy's, An advent to the Finite aspect process, 3rd variation is an replace of 1 of the most well-liked FEM textbooks to be had. The ebook keeps its powerful conceptual method, essentially studying the mathematical underpinnings of FEM, and offering a basic procedure of engineering software areas.
Known for its exact, rigorously chosen instance difficulties and vast number of homework difficulties, the writer has comprehensively lined quite a lot of engineering components making the publication approriate for all engineering majors, and underscores the big variety of use FEM has within the expert world.
A supplementary textual content website situated at http://www.mhhe.com/reddy3e comprises password-protected strategies to end-of-chapter difficulties, common textbook info, supplementary chapters at the FEM1D and FEM2D laptop courses, and extra!

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Extra resources for An Introduction to The Finite Element Method[Solutions]

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X ¯ = 0: ψ1 (0) = 1 → c1 = − Thus we have µ 3¯ x ψ1 (¯ x) = 1 − h ¶µ 3¯ x 1− 2h 9 2h3 (2) ¶µ x ¯ 1− h ¶ (3) Similarly, the Lagrange interpolation function for node 2 of a cubic element with equally-spaced nodes should be of the form, because it must vanish at x ¯ = 0, x ¯ = 2h/3 and x ¯ = h, where x ¯ is the local coordinate with the origin at node 1, ψ2 (¯ x) = c2 (¯ x − 0)(¯ x− 2h )(¯ x − h) 3 (4) The constant c2 is determined from the condition that ψ2 (h/3) = 1: c2 = we have µ ¶µ ¶ x ¯ 3¯ x x ¯ ψ2 (¯ x) = 9 1− 1− h 2h h 27 2h3 .

18a,b). Use the local coordinate x ¯ for simplicity. , x ¯ = 0: ψ1 (0) = 1 → c1 = − Thus we have µ 3¯ x ψ1 (¯ x) = 1 − h ¶µ 3¯ x 1− 2h 9 2h3 (2) ¶µ x ¯ 1− h ¶ (3) Similarly, the Lagrange interpolation function for node 2 of a cubic element with equally-spaced nodes should be of the form, because it must vanish at x ¯ = 0, x ¯ = 2h/3 and x ¯ = h, where x ¯ is the local coordinate with the origin at node 1, ψ2 (¯ x) = c2 (¯ x − 0)(¯ x− 2h )(¯ x − h) 3 (4) The constant c2 is determined from the condition that ψ2 (h/3) = 1: c2 = we have µ ¶µ ¶ x ¯ 3¯ x x ¯ ψ2 (¯ x) = 9 1− 1− h 2h h 27 2h3 .

The boundary conditions are U1 = 0 and Q32 = 1. 1420 The secondary variables can be computed using either the definition or from the element equations. 1 for the natural (or Neumann) boundary conditions µ ¶¯ du ¯¯ = 1, dx ¯x=0 µ ¶¯ du ¯¯ =0 dx ¯x=1 Use the uniform mesh of three linear finite elements to solve the problem. 1. The boundary conditions are Q11 = −1 and Q32 = 0. 10 are solved for the four nodal values ⎡ 52 −55 1 ⎢ −55 104 ⎢ ⎣ 0 −55 18 0 0 PROPRIETARY MATERIAL. 13272 U4 c The McGraw-Hill Companies, Inc.

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