A First Course in the Finite Element Method (4th Edition) by Daryl L. Logan

By Daryl L. Logan

A primary path within the Finite aspect research offers an easy, easy method of the finite point procedure that may be understood by means of either undergraduate and graduate scholars. It doesn't have the standard must haves (such as structural research) required through such a lot to be had texts during this zone. The e-book is written basically as a simple studying instrument for the undergraduate pupil in civil and mechanical engineering whose major curiosity is in tension research and warmth move. The textual content is aimed at those that are looking to practice the finite aspect process as a device to unravel sensible actual difficulties. This revised fourth version comprises the addition of a big variety of new difficulties (including SI problems), an appendix for mechanical and thermal houses, and extra civil functions.

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1 & ' 6 þ ' 7& d2x Àk2 F2x k2 6 k2 k1 k1 7 F2x ¼ ¼6 ð2:5:4Þ 7 4 1 d3x Àk2 k1 þ k2 F3x 1 5 F3x k1 k1 Now that d2x and d3x are known from Eq. 4), we substitute them in the first of Eqs. 2) to obtain the reaction F1x as F1x ¼ Àk1 d3x ð2:5:5Þ We can express the unknown nodal force at node 1 (also called the reaction) in terms of the applied nodal forces F2x and F3x by using Eq. 4) for d3x substituted into Eq. 5). The result is F1x ¼ ÀF2x À F3x ð2:5:6Þ Therefore, for all homogeneous boundary conditions, we can delete the rows and columns corresponding to the zero-displacement degrees of freedom from the original set of equations and then solve for the unknown displacements.

6, pp. 307–317, June 1991. , Liu W. , Nonlinear Finite Elements For Continua and Structures, John Wiley, 1996. 1 Define the term finite element. 2 What does discretization mean in the finite element method? 3 In what year did the modern development of the finite element method begin? 4 In what year was the direct stiffness method introduced? 5 Define the term matrix. 6 What role did the computer play in the use of the finite element method? 7 List and briefly describe the general steps of the finite element method.

1, No. 6, pp. 1437–1439, 1963. [20] Zienkiewicz, O. , and King, I. , ‘‘A Numerical Method of Visco-Elastic Stress Analysis,’’ International Journal of Mechanical Sciences, Vol. 10, pp. 807–827, 1968. [21] Archer, J. , ‘‘Consistent Matrix Formulations for Structural Analysis Using FiniteElement Techniques,’’ Journal of the American Institute of Aeronautics and Astronautics, Vol. 3, No. 10, pp. 1910–1918, 1965. [22] Zienkiewicz, O. , and Cheung, Y. , ‘‘Finite Elements in the Solution of Field Problems,’’ The Engineer, pp.

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