#Statics equilibrium 3d series#

After post-processing and structural manipulation, results have shown structures with a uniform load distribution on all members. This work proposes coupling topology optimization and graphic statics in a sequential framework to take advantage of both methods in generating truss-based designs and offering a way to manipulate such structures without breaking the global equilibrium state and reducing truss forces. Graphic statics is also a powerful platform for truss-based designs and, more importantly, manipulation of such designs to satisfy pre-defined structural/load constraints. Topology optimization is an effective tool for designing lightweight structures and truss-based designs. We give an overview of the well known procedure in 2D Graphic Statics to identify its key concepts and constructive elements, and describe the different steps of the three-dimensional version in detail.Ī combined topology optimization-graphic static approach is presented in this paper for manipulation and generation of equilibrium lightweight structures. The method, as it is presented here, is only applicable to statically determined systems of forces in which the applied loads do not generate a resultant couple. The procedure involves only geometric operations on polyhedral form and force diagrams. Therefore, in this paper, as a first step in the development of truly 3D Graphic Statics, we describe an equivalent procedure for given, three dimensional boundary conditions. One of the fundamental procedures in traditional (2D) Graphic Statics is to establish global equilibrium for given boundary conditions, and to use this information to construct different funicular solutions for the specified loads and supports. However, procedures for solving specific design and analysis problems with these polyhedral diagrams have not yet been developed.

It has been shown how the equilibrium of three-dimensional systems of forces can be described using polyhedral form and force diagrams.

#Statics equilibrium 3d series#

Only three-dimensional problems that can be replaced by an equivalent series of two-dimensional problems,Ĭan be addressed.

Unfortunately, the applicability of Graphic Statics to three-dimensional problems is limited. Graphic Statics provides a collection of procedures for the design and analysis of two-dimensional structural systems, involving only geometric operations on two-dimensional form and force diagrams.