By William R. Spillers
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Extra resources for Automated Structural Analysis. An Introduction
While the assembly of elements can be handled in a rather routine manner, as this book attemps to show, the meaningfulness of the results obtained is a direct product of the member descriptions used and must stand or fall on their validity. The behavior of an individual element can be approached on any level of sophistication, mathematically or experimentally. It would surely be inconsistent with the objectives of this book, one of which is simplicity, to deal with the continuum mechanical aspects of member stiffness.
3 generalizes for members with three and four nodes (triangular and quadrilateral finite elements). 2. Show how the formulation of the node method changes when the order of the components of either, but not both, of the node force matrix or the node displacement matrix is changed. Answer: Since the truss is the only structure already discussed in detail in this text, it will be used to discuss this exercise. , member displacements for the frame. ); Pi = (Pi), (Pi)x. it would be necessary to use a permutation matrix to maintain the physical interpretation of work and energy.
The behavior of an individual element can be approached on any level of sophistication, mathematically or experimentally. It would surely be inconsistent with the objectives of this book, one of which is simplicity, to deal with the continuum mechanical aspects of member stiffness. In fact, only the use of straight, uniform members is discussed in any detail here. On the surface this would appear to be a considerable restriction. In this chapter it is shown how a good deal of generality can be achieved through the use of straight uniform members to approximate an arbitrarily curved member.
Automated Structural Analysis. An Introduction by William R. Spillers