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This paper presents an optimization procedure for the solution of the planarity problem, a requirement of grid shells with four or more sides faces that need of having four adjacent nodes laying on a plane in order to use plane glass slabs as cladding elements. It can be satisfied by applying specific geometric rules in the grid generation phase but, when the architectural shape is already defined at the conceptual stage, an optimization procedure can yield to suitable configurations. A Relaxation method based on nodal planarity errors and an evolutionary population based Genetic Algorithm have been applied to set of benchmarks, in order to tune parameters and to obtain general information about the solution. the problem and their efficiency compared. The Relaxation method in general shows better efficiency in reaching optimal solutions, as an effect of the regularity of the target function. The Genetic Algorithm, on the other hand, performs a wider exploration of feasible solutions, generating unexpected sub-optimal configurations.
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... j.cai@seu.edu.cn equilibrium path by many researchers (Forman and Hutchinson 1970, Gosowski 2003, Gioncu 1995, Liu et al. 2015, Meek and Tan 1984, Nie 2003, Sassone and Pugnale 2010, Zhang et al. 2013, Zhou et al. 2014). The structural behavior of the shell structures during the whole loading process can be described by the load- deflection curves which then give the buckling load. ...
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