Literally, a pneumatic membrane structure is a gas-filled type inflatable membrane whose interaction of the surrounding membrane and the enclosed gas (fluid) determines
its responses at any instance. Numerical algorithms to solve such problems are challenging due to their highly nonlinearity and nonsmoothness. Within this work, the mathematical
description for continuum mechanics is used to explain three major nonlinearities involved in the inflatable membrane: wrinkling, pressure loads and contact. Based on the
finite element discretization, numerical treatment and solution techniques are provided regarding numerical accuracy, robustness and stability.
First, the wrinkling phenomenon is a key characteristic of a thin membrane which reacts to compressive stresses beyond its capability by means of the local buckling “waves” to release
excessive compressive stresses. Since geometric representation of these little waves by finite elements is costly, this work proposed two efficient wrinkling models based on modifications of material laws: the projection and plasticity analogy models. Besides deeming wrinkling as a sub-grid phenomenon beneath the scale of finite element mesh, they provide asymptotically accurate stress fields corresponding to existing wrinkles.
Secondly, influences of pressure applied to a surface of a membrane are taken into account by the deformation-dependent load definition which leads to both nominal load stiffness, caused by the change in surface normal, and additional load stiffness, originated from the change in pressure magnitude. In certain circumstances, the system matrix is turned to a fully populated one where a suitable solution technique is introduced to handle this
pathological situation effectively for both quasi-static and dynamic analyses to improve the convergence rate and numerical accuracy.
Lastly, to deal with issues of large deformation contact for the inflatable membranes, a mortar-based contact formulation is derived such that the imprenetrability condition is defined in an integral manner over the contact area as well as the Lagrange multiplier interpolated by dual basis functions is used to enforce the contact conditions in the weak sense
to achieve an efficient approach regarding to the robustness and accuracy. Furthermore, the discrete velocity update is introduced upon existing stable time integration methods to
achieve an energy conservative solution technique for the contact problem of interest.
Various numerical simulations provide adequate proof of utilities for the presented approaches.
By the capability to take into account simultaneously all mentioned nonlinear behaviors, the proposed algorithm has high potential with further developments for more
complicated issues.
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Literally, a pneumatic membrane structure is a gas-filled type inflatable membrane whose interaction of the surrounding membrane and the enclosed gas (fluid) determines
its responses at any instance. Numerical algorithms to solve such problems are challenging due to their highly nonlinearity and nonsmoothness. Within this work, the mathematical
description for continuum mechanics is used to explain three major nonlinearities involved in the inflatable membrane: wrinkling, pressure loads and co...
»