Direct area minimization through dynamic relaxation

Minimal surfaces, characterized by the property of a minimal area within a fixed boundary, offer an interesting design option for membrane structures, since they are uniquely defined and provide economy of material and more regular fabric patterns. Analytical solution for the non-linear equation governing area minimization may be rather difficult for complex boundaries, leaving numerical solution as the only general way to tackle with the problem. In this paper we show that the dynamic relaxation method offers an interesting alternative to solve the area minimization problem, first interpreted as a nonlinear equilibrium problem, then replaced by a pseudo-dynamic analysis, where fictitious masses and damping matrices are arbitrarily chosen to control the stability of the time integration process

Implementation of a simple wrinkling model into argyris’ membrane finite element

This paper presents the implementation of a simple wrinkling/slackening model into the classical Argyris membrane element, comparing the solution performance by Newton’s iterations, using either the tangent stiffness matrix (numerically evaluated through a finite-difference approximation), or a secant stiffness matrix (obtained through the modification of the elasticity matrix, according to a projection technique which decompose deformations into elastic and wrinkle components)

Direct area minimization through dynamic relaxation

Minimal surfaces, characterized by the property of a minimal area within a fixed boundary, offer an interesting design option for membrane structures, since they are uniquely defined and provide economy of material and more regular fabric patterns. Analytical solution for the non-linear equation governing area minimization may be rather difficult for complex boundaries, leaving numerical solution as the only general way to tackle with the problem. In this paper we show that the dynamic relaxation method offers an interesting alternative to solve the area minimization problem, first interpreted as a nonlinear equilibrium problem, then replaced by a pseudo-dynamic analysis, where fictitious masses and damping matrices are arbitrarily chosen to control the stability of the time integration process

Implementation of a simple wrinkling model into argyris’ membrane finite element

This paper presents the implementation of a simple wrinkling/slackening model into the classical Argyris membrane element, comparing the solution performance by Newton’s iterations, using either the tangent stiffness matrix (numerically evaluated through a finite-difference approximation), or a secant stiffness matrix (obtained through the modification of the elasticity matrix, according to a projection technique which decompose deformations into elastic and wrinkle components)

Modeling sliding cables and geodesic lines through dynamic relaxation

p. 2047-2058The Dynamic Relaxation Method (DRM) is an interesting alternative to solve complicated nonlinear equilibrium problems, solved via a pseudo-dynamic analysis, with explicit time integration, carried out exclusively by fast vector manipulations. In the current paper, we present the theoretical formulation and the implementation of the load vectors of a class of finite elements capable of representing the slippage between border cables and membrane sheaths, without friction. The paper also details some improvements in a procedure to search geodesic lines onto triangle-faceted surfaces, relating the expression of the internal load vector of the geodesic string element to the internal vector of a sliding-cable superelement, and proposing a new average nodal normal vector, insensitive to the arbitrary division of a given geometry into different triangular meshes.Pauletti, RMO.; Guirardi, DM.; Gouveia, S. (2010). Modeling sliding cables and geodesic lines through dynamic relaxation. Editorial Universitat Politècnica de València. http://hdl.handle.net/10251/724