Numerical Error in Structural Solutions

Numerical error may destroy the significance of the results of a structural analysis, particularly for certain classes of structures. The initial truncation error originating from representing each value of the structural matrices to constant computer word length approximates the total numerical error in the solution for displacements in medium-sized problems. An upper bound for this error can be readily calculated, and is usually not too conservative when the global stiffness matrix is scaled before solution. When this error appears too large, only consistent higher precision representation and solution of the various structural matrices will ensure a more accurate solution. The varying accuracy of the displacements due to different loading conditions on the same structure is rigorously explained. The normal expression for the a posteriori error bound on the solution is unreliable as it omits the effect of initial truncation in representing the global stiffness matrix. Flexible areas within generally stiff structures and stiff areas within generally flexible structures can both lead to inaccurate solutions for displacements throughout the structure.