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Abstract

A load bearing structure having a set of uniform voids functions to resolve the forces imposed by developing compression in the material having the voids and minimizing the amount of tension developed in the material. For the voids to have this function, they must be deployed in a particular fashion. The voids are deployed to encompass a particular set of points. The set of points are such that each point in the matrix is spaced an equal distance from twelve and only twelve adjacent points of the matrix. The distance between the points does not matter as long as all are uniformly distanced in accordance with that rule. If the structure is considered to be composed of a closely packed set of hypothetical rhombic dodecahedra (RD) and the four edge vertices of each of those hypothetical RDs is truncated, the result will be a set of cubic voids. The center of each of those cubic voids will define the matrix referred to above and the cubic voids will serve to provide the optimum resolution of stress which minimizes the development of tension in the material. One in four of the hypothetical or mathematical RDs can be eliminated achieving the same force resolution result in a structure that contains less material. The shape and size, but not the position, of the voids can be varied with only slight loss in optimum stress resolution. Some voids can be omitted with only slight loss of optimum stress resolution.

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