engleski

An Extended Linear Procedure for Constrained Form Finding

The execution time of the form nding algorithm plays a key role in the performance of the interactive form nding tool. Therefore, enhanced by the idea of establishing an algorithm that would answer the need for fast calculation, the paper presents the extension of iterative application of the force density method, originally used for design and internal force evaluation of tensile structures. Preserving the bene ts of the initial linear procedure, the presented extension focuses on both the acceleration of the method and the greater in uence on the appearance of the nal solution in the form nding problems with design constraints. In order to achieve a reduction in the number of iteration steps, and consequently a reduction in the execution time, tolerance optimisation for solving the system of equilibrium equations in each iteration step is introduced. For more control over the structures geometry, in addition to force and length constraints from the initial setup of the algorithm, the ability to assign unstrained lengths of elements is enabled. Form nding of several cable nets is conducted in order to compare the performance of the proposed procedure against the original method, and to show the potential of using unstrained length constraints in in uencing the nal geometry of the structure.

constrained form finding ; constrained force density method ; iterative methods ; tolerance optimisation ; time comparison ; system of linear equations ; cable-nets ; unstrained length constraint

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