7R2. An Introductory Guide to Finite Element Analysis.- Edited by AA Becker (Dept of Mech Eng, Univ of Nottingham). ASME International, New York. 2004. 171 pp. Hardcover. ISBN 0-7918-0205-1. $79.00.
Reviewed by D Karamanlidis (Dept of Civil Eng, Univ of Rhode Island, Bliss Hall, Kingston RI 02881).
As anyone who ever taught or took a course on finite elements will attest, there is no short supply on introductory texts on Finite Element Analysis (FEA). In fact, there must be over a hundred such texts currently in print and several of them are nothing short of excellent. On the top of this reviewer’s list are (in no particular order) Segerlind, Huebner, Bathe, and Wilson, Gallagher, Yang, Desai and Abel, and others. Thus, with so many good books to choose from the following question arises: What does a new FEA text need to offer in order to have a chance against all these well-established, time-honored heavyweights? The key, in the opinion of this reviewer, is pedagogy. Present the subject in such a way that today’s undergraduates (with a relatively limited experience in math and mechanics) can grasp the salient concepts behind the method.
According to the preface, “the book is suitable both for beginners and those seeking to strengthen their background knowledge of FE methods.” It is broken down in ten chapters, namely: 1) Introduction and background, 2) Structural analysis using pin-jointed elements, 3) Continuum elements, 4) Energy and variational principles, 5) Higher order quadratic elements, 6) Beam, plate, and shell elements, 7) Practical guidelines for FE applications, 8) Introduction to nonlinear FEA, 9) Thermal Problems, 10) Examples of FE applications. Chapters 1 through 9 contain a combined total of three (3) examples and not a single assignment problem.
Now taking a closer look at the contents, one is puzzled by the sheer volume of omissions, misrepresentations and confusing statements that made the final print. Some examples are listed below:
Page 9, Strain Energy: Concerning the formula, in Equation (1.14) the integration symbol is missing and should be replaced by. In the next equation on the same page, the factor 1/2 is missing.
Page 14: In both equations (1.30) and (1.31), the factor 2 is missing in front of the shear terms.
Pages 17 and 19: Equation (2.2) states that the axial strain for a rod is given by whereas Equation (2.13) leads to.
Page 19: With reference to the two-noded truss element, it stated that “such an element is said to have one degree of freedom.” Actually, the element is known to have two degrees of freedom (=independent displacements), namely u1 and u2.
Page 26: Concerning the stiffness matrix for the two-noded truss element using global displacement variables, it is stated that it is derived by taking the partial derivatives of the strain energy in terms of the four global displacements. Since these four variables are linearly dependent, the above operation is not permissible.
Boundary Conditions: The reader comes away with the impression that first the global stiffness matrix is assembled and then the boundary conditions are imposed. Actually, it is common practice to impose the boundary conditions on the fly during the assembly thereby avoiding the need to unnecessarily inflate both the size of the global equations and the computational effort to solve them (cf, Bathe and Wilson, to name but one source).
Continuum Elements: Only the stiffness matrix for the time-honored but nowadays rarely used CST element is presented. Nothing about quadrilateral elements, not to mention isoparametric elements. This is a bit strange, because the results presented in Chapter 10 were actually produced using isoparametric elements.
Page 57: With reference to solutions obtained using Ritz method, it is stated that “the above exact solution is different from all the trial solutions used above." Actually, Equations (4.21) (trial solution) and (4.24) (exact) are identical.
Beam Element: The beam shape functions may be written down directly as Hermitian polynomials. There is no need to invert any 4×4 matrices to obtain them. It’s not clear to this reviewer why not a single example was presented to showcase the element’s use.
Plate/Shell Elements: Given the fact that these are the most widely used elements, it’s not clear why only the special cases of axisymmetric elements (which are very similar to the previously presented beam and truss elements) are mentioned.
Further, the choice to include a superficial at best coverage of nonlinear FEA (let’s face it: others have devoted to the subject two volumes double the size of the present one) instead of more down the earth topics such as buckling and free vibrations) appears to be a curious one.
In conclusion, it is the opinion of this reviewer that An Introductory Guide to Finite Element Analysis suffers from too many deficiencies to be considered suitable reading both for beginners and those seeking to strengthen their background knowledge of FE methods. Students and instructors interested in FEA will be better off sticking with the classics mentioned previously.