SUMMARYThis paper illustrates a method whereby a family of robust equilibrium elements can be formulated in a general manner. The effects of spurious kinematic modes, present to some extent in all primitive equilibrium elements, are eliminated by judicious assembly into macro-equilibrium elements. These macroelements are formulated with sufficient generality so as to retain the polynomial degree of the stress field as a variable. Such a family of macro-elements is a new development, and results for polynomials of degree greater than two have not been seen before. The quality of results for macro-equilibrium elements with varying degrees of polynomial is demonstrated by numerical examples.
A class of problems in the geometric optimization of yield-line patterns, for which the currently advocated conjugate gradient and sequential linear programming geometric optimization algorithms fail is investigated. The Hooke-Jeeves direct search method is implemented and is demonstrated to solve such problems robustly.
SUMMARYA comparative study of error estimators using a patch recovery scheme with those using simple nodal averaging is made for the four-noded Lagrangian quadrilateral element through two plane stress elasticity problems. It is demonstrated that error estimators using a patch recovery scheme are generally more effective and have an estimated stress field that is closer to the exact one than those using simple nodal averaging.KEY WORDS error estimation; super convergent patch recovery scheme
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