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Form Finding of Shell Structures by Using Membrane Theory

Advanced Structured Materials, ISSN: 1869-8441, Vol: 127, Page: 213-237
2021
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Book Chapter Description

A two-step form-finding strategy for determining the heights of a shell of a given plan-form is presented. The shell heights are determined in such a way that the structure can equilibrate applied loads by pure membrane actions. To this end, a set of algebraic equations are obtained by applying the finite difference method to the differential equations derived from the membrane theory of shells. The two-step procedure amounts to compute a distribution of projected membrane stresses that fulfil assigned boundary conditions and to compute shell heights as a function of the membrane stresses computed at the previous step. In case the loads are known in advance, the shell heights are computed in closed form, while the procedure is iterative if loads are expressed as a function of the shell heights. Two numerical examples show the feasibility of the proposed approach.

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