TABLE OF CONTENTS In the preceding chapters, computational procedures have been described that yield structural deformations for linear and nonlinear problems subjected to static and also dynamic time-dependent mechanical and thermal loading. Stresses in various elements in the structure due to nodal deflections may be calculated to check if the structure can safely withstand the externally applied load. Typically the process first includes computation of element nodal deflections in the LCS from values already computed in the GCS. These values are then used along with the element strain transformation and constitutive matrices derived in their LCS to compute element stresses. Thus element stress computation involves the following steps. [1] , [2] , [3]
Step 1: Obtain element node deflections from global values
Step 2: Compute element strains from the strain displacement relationship
Step 3: Compute element stresses from strains with the appropriate constitutive law
The derivations for a number of elements are given next, followed by details on structural optimization.
[1]Timoshenko S., and Goodier, N., Theory of Elasticity, 3rd ed., McGraw-Hill, New York, 1951.
[2]Timoshenko S., and Woinsowsky-Krieger, S., Theory of Plates and Shells, 2nd ed., McGraw Hill, New York, 1959.
[3]Przemieniecki, J. S., Theory of Matrix Structural Analysis, McGraw-Hill, New York, 1968.
The following steps are necessary for the computation of stresses in a line beam element.
Step 1: Obtain element nodal deformations in LCS
in which
and ? is the element direction cosine matrix.
Step 2:
