Premium
Application of non‐linear programming to optimum grillage design with non‐convex sets of variables
Author(s) -
Kavlie Dag,
Moe Johannes
Publication year - 1969
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620010404
Subject(s) - statically indeterminate , mathematics , minification , regular polygon , mathematical optimization , linear programming , metric (unit) , variable (mathematics) , minimum weight , plane (geometry) , convex optimization , structural engineering , algorithm , engineering , geometry , combinatorics , mathematical analysis , operations management
Abstract The application of non‐linear programming methods for the optimum design of statically indeterminate structures is discussed, with special emphasis on the design of elastic grillages loaded laterally and in plane. Some features of SUMT (sequential unconstrained minimization technique) are demonstrated by means of numerous examples of varying complexity. The Variable Metric method of search is discussed and compared to Powell's Direct Method. It is shown that non‐convex sets of design variables are often encountered in structural problems of the grillage type. SUMT may still be used, but the choice of starting value and initial response factor decisively influences the chance of finding the global optimum. It is demonstrated that a fully stressed design may not necessarily correspond to the minimum weight design. Optimum design of grillages which are simultaneously subjected to lateral and in‐plane loads may be performed efficiently by means of non‐linear programming.