Continuum modeling of three-dimensional truss-like space structures

A mathematical and computational analysis capability has been developed for calculating the effective mechanical properties of three-dimensi onal periodic truss-like structures. Two models are studied in detail. The first, called the octetruss model, is a three-dimensional extension of a two-dimensional model, and the second is a cubic model. Symmetry considerations are employed as a first step to show that the specific octetruss model has four independent constants and that the cubic model has two. The actual values of these constants are determined by averaging the contributions of each rod element to the overall structure stiffness. The individual rod member contribution to the overall stiffness is obtained by a three-dimensional coordinate transformation. The analysis shows that the effective three-dimensional elastic properties of both models are relatively close to each other. HE past decade has witnessed a dramatic increase in the research activities dealing with the possibility of utilizing space for commercial and scientific needs. Recently, many articles1"4 have appeared which deal with diverse aspects of large space structures. These articles have identified various applications and also proposed novel designs of structures to meet such applications. A review of the research activities on space structures prior to 1966 has been documented in the excellent volume5 that resulted from the International Conference on Space Structures. It thus has become necessary to find and analyze small, lightweight three-dimensional structures that will be used easily to construct much larger space structures. It would be desirable for these structures to be isotropic in nature. However, construction requirements may make this in- feasible, therefore requiring orthotropic or possibly com- pletely anisotropic structures. The latter is also undesirable because of the added complexity to the problem. Truss-type periodic (repetitive) structures recently have been suggested and analyzed as candidates for space structures.6'7 Here simplicity in construction coupled with large stiffness-to- density ratios will be most desirable. The objective of the present paper is to develop analytical and computational analysis capabilities in order to generate equivalent continuum elastic properties for three-dimensional truss-like periodic structures. Broadly speaking, we outline the method as follows. Once the geometry of the repeating cell of the structure is identified, symmetry arguments are em- ployed as a first step to identify the independent elastic coefficients. The actual values of these constants are deter- mined by averaging the contribution of each rod element to the overall structure stiffness. The individual rod member contribution is obtained by a three-dimensional coordinate transformation. In this context, the use of the transformation relations to generate effective properties of lattice plates has been utilized by Heki. 8 In order to assess the utility of our analysis, we shall specialize our results to the following two candidate structures. The first is a three-dimensional