Finite element analysis punishes a particular kind of student: the one who can run the software. A First Course in the Finite Element Method, Enhanced Edition, 6th Edition by Daryl L. Logan spends its early chapters assembling stiffness matrices by hand precisely so that the mesh stops being a black box, and coursework then examines the understanding rather than the output. Where students come unstuck is the gap between arithmetic and judgment — assembling a global matrix correctly but not seeing why it is singular before restraints, or choosing an element without asking what its shape functions can actually represent.
Why this test bank helps
Reaching the right answer is half the value; being able to state the principle it rests on is what carries over to a problem you have not seen. Every question in this set is followed by a written rationale that works through the reasoning — which assumption of the formulation is in play, what the matrix property means physically, and why each of the other options describes a different element, a different boundary condition or a different source of error.
What’s inside
- Questions organized chapter by chapter, from the direct stiffness method through to dynamic analysis.
- Conceptual multiple-choice items alongside short numerical questions on stiffness terms, degrees of freedom and matrix assembly.
- A written rationale under every item, explaining the principle rather than just restating the arithmetic.
- Deliberate emphasis on modeling judgment: element choice, mesh refinement, convergence and interpreting results.
- A single organized PDF, downloadable as soon as checkout completes.
Topics covered
- The direct stiffness method — spring and bar elements, element and global stiffness matrices, assembly, and applying boundary conditions.
- Trusses and frames — coordinate transformation, two- and three-dimensional truss analysis, beam elements, distributed loading and frame assembly.
- Energy and weighted-residual formulations — potential energy methods, Galerkin’s method, and the variational basis of the element equations.
- Plane stress and plane strain — the constant-strain triangle, linear-strain triangle, and the derivation of element stiffness for two-dimensional problems.
- Isoparametric formulation — natural coordinates, shape functions, the Jacobian, and numerical integration by Gaussian quadrature.
- Axisymmetric and three-dimensional elements — the axisymmetric formulation, tetrahedral and brick elements, and their computational cost.
- Field problems — one- and two-dimensional heat transfer, fluid flow and other problems governed by the same governing form.
- Dynamics and modeling practice — mass matrices, natural frequencies and mode shapes, convergence, aspect ratio, mesh refinement and common modeling errors.
Who it’s for
Undergraduate and beginning graduate students in mechanical, civil or aerospace engineering taking a first finite element course from this edition, and practicing engineers refreshing the theory behind commercial analysis packages.
How to use it (the right way)
Work the chapter’s own problems first, then use these questions closed-book to check whether you understood the formulation or only followed the algebra. Read the rationale on everything you missed, and sketch the element whenever a question describes one. This is a study aid, to be used in line with your institution’s academic-integrity policy — for preparation and self-testing, not as a shortcut around the coursework or as material carried into a graded assessment.
Sample question (shows the format — your download contains the full set)
Q. Before any boundary conditions are applied, the assembled global stiffness matrix of a structure is singular. What does this indicate?
- A. An error was made during assembly of the element matrices.
- B. The structure is unrestrained, so rigid-body motion is still possible.
- C. The chosen elements are too coarse and the mesh must be refined.
- D. The material stiffness has been entered as zero.
Answer: B. With no supports specified, the model can translate or rotate as a rigid body without any strain energy, so a set of nonzero displacements produces zero force and the matrix has no inverse; applying enough restraints to eliminate rigid-body modes makes it nonsingular. A is wrong because a correctly assembled unrestrained matrix is expected to be singular — the singularity is a property of the physics, not evidence of a mistake. C confuses accuracy with solvability; a coarse mesh gives a poor answer, not an unsolvable system. D would be a data error producing a different symptom and is not implied by singularity alone.
Edition & format
- Matches: A First Course in the Finite Element Method, Enhanced Edition, 6th Edition, by Daryl L. Logan.
- Format: Digital PDF, delivered instantly after checkout.
- Access: Lifetime — re-download from your account whenever you need it.
The enhanced printing and the standard printing are numbered differently in places. Please confirm the edition and ISBN of your own copy match this listing before buying.
Frequently asked questions
Is this the current edition? This set is prepared against the 6th Edition, enhanced printing. If your course lists a different edition, choose that listing instead, since chapter and problem numbering change.
How do I receive it? The download link appears on your order confirmation page and in your account as soon as checkout completes. Nothing is shipped.
Do all the questions include rationales? Yes. Every item carries a written explanation of the principle behind the keyed answer and the faults in the alternatives.
Is using a test bank allowed? As a study aid it works like any other practice resource. Follow your institution’s academic-integrity policy and never take the material into a graded assessment.
More titles for this course are in Engineering Test Banks.
Reviews
There are no reviews yet.