Parametric design of purely compressed shells

Within the frame of parametric design, in the present work we focus on a very special objective, namely parametrically generating families of purely compressed shells. A similar task can be pursued by adopting for the equilibrium analysis the so-called Thrust Network Analysis for which the shell structure is condensed into a network of bars. Here instead, we adopt a continuum approach, namely the so-called Membrane Equilibrium Analysis. With this continuum approach, a purely compressed membrane equilibrium solution is searched by solving a scalar second-order partial differential equation representing the transverse equilibrium equation of the membrane. The shell is compressed if the membrane surface is contained within the volume of the shell and if the stress potential is concave. For a given shell, the main difficulty is represented by the fulfillment of the concavity constraint for the stress potential. In the present study, this difficulty is overcome by assigning families of convenient concave stress potentials and considering the shape as the unknown. By considering stress potentials or boundary data controlled by a few parameters, such variable parameters can be manipulated in order to alter the end result. Other methods tackling the stress function with the help of a computer, exist in the literature, but the main contribution of the present paper is the shape analysis of compression-only shells with the help of finite element apparatus. A few illustrative examples are presented to demonstrate the method. •Parametric design of compressed membrane shapes.•Shapes associated to special classes of stress potentials: from stress to shape.•Variational-Finite Element Formulation of the membrane equilibrium governing equations.•Applications to the case of smooth and singular coefficients of the pde.