An efficient numerical shape analysis for light weight membrane structures

Abstract

Abstract:The determination of initial equilibrium shapes is a common problem in research work and engineering applications related to membrane structures. Using a general structural analysis framework of the finite particle method (FPM), this paper presents the first application of the FPM and a recently-developed membrane model to the shape analysis of light weight membranes. The FPM is rooted in vector mechanics and physical viewpoints. It discretizes the analyzed domain into a group of particles linked by elements, and the motion of the free particles is directly described by Newton's second law while the constrained ones follow the prescribed paths. An efficient physical modeling procedure of handling geometric nonlinearity has been developed to evaluate the particle interaction forces. To achieve the equilibrium shape as fast as possible, an integral-form, explicit time integration scheme has been proposed for solving the equation of motion. The equilibrium shape can be obtained naturally without nonlinear iterative correction and global stiffness matrix integration. Two classical curved surfaces of tension membranes produced under the uniform-stress condition are presented to verify the accuracy and efficiency of the proposed method.

How to Understand 'Structural Morphology'?

“…Based on the mechanical concept of the vector form intrinsic finite element [16], Yang et al [17] presented a general finite particle method (FPM) framework for investigating the shape analysis of tension membrane structures under given boundary conditions. If this method is applied iteratively with constant and isotropic stress prescribed at any given point on the surface, it can lead to a stable minimal surface.…”

Active structures integrated with wireless sensor and actuator networks: a bio-inspired control framework

“…(37) is not required to contain those arguments. From the point of computation, the equation of motion (1) can be solved by a simple explicit time integration, such as the central difference method (Bathe and Wilson, 1976;Luo and Yang, 2014;Yang et al, 2014). The variation of nodal displacement is assumed to consist of a series of straight-line segments, and the nodal velocity between two time points is assumed to be constant (Fig.…”

A vector-form hybrid particle-element method for modeling and nonlinear shell analysis of thin membranes exhibiting wrinkling

“…It contents four fundamental concepts: (a) point value description, (b) path unit description, (c) a kinematical description of particle motion and deformation by incorporating an adaptive convected material frame, and (d) strong formed equations of motion governed by Newton's second law. For a further discussion about these subjects, one can consult references Ting et al, 2004;Yu, 2010;Yang et al, 2014) where a complete and detailed vision can be found.…”

“…In this work, these interaction forces are modeled by a set of triangular shell elements connected with particles, and thus the stress state of this kind of elements can be considered as a simple superposition of the membrane stress and the plate bending stress. Regarding the evaluation of the former effect caused by the in-plane deformation of the mid-surface, the detailed formulations can be found in our former work of shape analysis of membranes (Yang et al, 2014) and does not specify here in depth. This section is focused on the derivation for the formulations of particle interaction forces related to the non-zero bending rigidity of a membrane, i.e., the moments.…”

“…3a, for deducting the rigid body motions from the total displacement and rotation increments of particles. Yang et al (2014) exhaustively discussed the fictitious reverse motion and provided the detailed derivations of the rotation angle and the corresponding direction vector of rotation axis e . Thus, the deformation displacement vector of node i from t a to t can be evaluated by…”