This paper presents an automatic process for fabrication-oriented design of custom-shaped rubber balloons. We cast computational balloon design as an inverse problem: given a target shape, we compute an optimal balloon that, when inflated, approximates the target as closely as possible. To solve this problem numerically, we propose a novel physics-driven shape optimization method, which combines physical simulation of inflatable elastic membranes with a dedicated constrained optimization algorithm. We validate our approach by fabricating balloons designed with our method and comparing their inflated shapes to the results predicted by simulation. An extensive set of manufactured sample balloons demonstrates the shape diversity that can be achieved by our method. © 2012 Wiley Periodicals, Inc.

Computational Design of Rubber Balloons

NiftySim, an open-source finite element toolkit, has been designed to allow incorporation of high-performance soft tissue simulation capabilities into biomedical applications. The toolkit provides the option of execution on fast graphics processing unit (GPU) hardware, numerous constitutive models and solid-element options, membrane and shell elements, and contact modelling facilities, in a simple to use library. The toolkit is founded on the total Lagrangian explicit dynamics (TLEDs) algorithm, which has been shown to be efficient and accurate for simulation of soft tissues. The base code is written in C
 $$++$$
 , and GPU execution is achieved using the nVidia CUDA framework. In most cases, interaction with the underlying solvers can be achieved through a single Simulator class, which may be embedded directly in third-party applications such as, surgical guidance systems. Advanced capabilities such as contact modelling and nonlinear constitutive models are also provided, as are more experimental technologies like reduced order modelling. A consistent description of the underlying solution algorithm, its implementation with a focus on GPU execution, and examples of the toolkit’s usage in biomedical applications are provided. Efficient mapping of the TLED algorithm to parallel hardware results in very high computational performance, far exceeding that available in commercial packages. The NiftySim toolkit provides high-performance soft tissue simulation capabilities using GPU technology for biomechanical simulation research applications in medical image computing, surgical simulation, and surgical guidance applications.

/pdf/niftysim-a-gpu-based-nonlinear-finite-element-package-for-hlyh3ddzgi.pdf

NiftySim: A GPU-based nonlinear finite element package for simulation of soft tissue biomechanics

Designing engineering components that make optimal use of materials requires consideration of the nonlinear static and dynamic characteristics associated with both manufacturing and working environments. The modeling of these characteristics can only be done through numerical formulation and simulation, which requires an understanding of both the theoretical background and associated computer solution techniques. By presenting both the nonlinear solid mechanics and the associated finite element techniques together, the authors provide, in the first of two books in this series, a complete, clear, and unified treatment of the static aspects of nonlinear solid mechanics. Alongside a range of worked examples and exercises are user instructions, program descriptions, and examples for the FLagSHyP MATLAB computer implementation, for which the source code is available online. While this book is designed to complement postgraduate courses, it is also relevant to those in industry requiring an appreciation of the way their computer simulation programs work.

Nonlinear Solid Mechanics for Finite Element Analysis: Statics

https://orbilu.uni.lu/bitstream/10993/16438/1/2014_NURBSbasedExplicit_Membranes_CMAME_.pdf

Explicit finite deformation analysis of isogeometric membranes

In this paper, finite axisymmetric inflation of an initially stretched flat circular hyperelastic membrane has been analyzed. The membrane material has been assumed to be a homogeneous and isotropic Mooney–Rivlin solid. The inflation problem has been reduced to a set of three first order ordinary differential equations using a set of appropriately defined variables. An interesting method based on the invariance of these equations to scaling has been used to solve the two point boundary value problem without much effort. This method does not require any special technique for negotiating the limit points in the pressure–stretch relations of the membrane. Several inflation results of an initially unstretched and pre-stretched circular membrane for various material parameters are obtained. The roles of pre-stretch and internal pressure on the inflation mechanics are clearly delineated. The initial stretch is observed to have some interesting counter-intuitive effects on the inflation of the membrane.

P. Heywood

Papers

Finite element analysis of air supported membrane structures