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Title: Structural analysis of prestressed Saint Venant-Kirchoff hyperelastic membranes
Author: Gil, A. J.
Awarding Body: University of Wales Swansea
Current Institution: Swansea University
Date of Award: 2004
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A total Lagrangian formulation for prestressed structural membranes is described. The kinematics of prestressed membranes is displayed as a series of three successive configurations, namely, a nominally stressed initial equilibrium state R0, a prestressed state Rpret and a final in-service state R, for the time instants t0, tpret and t, respectively. Kinematic entities are fully derived, i.e., deformations gradient tensor, displacement gradient tensor, right Cauchy-Green tensor or Green-Lagrange strain tensor. Among the wide group of available hyperelastic materials to describe moderate strain behaviour, the Saint Venant-Kirchoff model is chosen as the most adequate. By following its definition, the Helmholtz’s free energy functional or strain energy functional wint is used a s potential in order to obtain the second Piola-Kirchhoff stress tensor. Alternative stress tensors such as the Cauchy stress tensor or the first Piola-Kirchhoff stress tensor are derived as well. Another physical feature that is taken into account is the likelihood of developing wrinkles. The proposed technique in order to capture wrinkles attempts to develop a set of conditions in terms of the Euler-Lagrange strain tensor along its principle directions. Subsequently, a modified Helmholtz’s free energy functional will be introduced with the purpose of describing in an alternative manner the constitutive behaviour of the continuum medium after the moment of wrinkling. The Force Density Method is reviewed in order to determine initial shapes for tension structures. These equilibrium shapes are employed as initial guesses for the subsequent highly nonlinear problem that entails the structural analysis of the membrane under the actual presence of prestressing loading and external loading.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available