Mechanically rational forms of curved surface structures shaped from the uniform strain elements

Abstract

The paper proposes a method for finding mechanically rational and practical forms of curved surface by using the uniform strain elements. Numerical methods for form finding already published give exact solutions but the application is restricted to the problems with the conditions possible to form a minimal surface. This is because the methods use the mechanical model without material stiffness but with only the geometric stiffness of isotropic tension. When the uniform strain elements composing a structural form have even isotropic strain in all over the form, the form is an isotropic tension form. Since the uniform strain element has the material stiffness, the method can stably yield a form with the strains varying as narrowly as possible in the curved surface under the condition impossible to shape a minimal surface.