Finite element modeling of orthotropic material behaviour in pneumatic membranes

Raible, T.; Reese, Sven H.; Wriggers, Peter

doi:10.1002/zamm.20000801476

Cited by 8 publications

(10 citation statements)

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“…In the formulation of the implemented polyconvex orthotropic term, unlike the typical multiplicative non-polyconvex ones [ 23 , 26 ], the notion of anisotropic metric tensor

is utilized as the so-called structural tensor. In general, the full component metric tensors are able to describe generic classes of anisotropy which at the same time may preserve the polyconvexity condition of the energy density functions [ 22 ].…”

Section: Elastic Materials Models For Textile Membranes and Parametmentioning

confidence: 99%

The Elastic Share of Inelastic Stress–Strain Paths of Woven Fabrics

et al. 2020

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Manifold variations of the mechanical behavior of structural woven fabrics appear in the first load cycles. Nevertheless, invariable states, i.e., mechanically saturated states, can be approached by multiple monotonous load cycle biaxial tests. In a state acceptably close to the ideal saturated state, the stress–strain paths reveal the elastic share of the initially inelastic stress–strain paths of woven fabrics. In this paper, the mechanical saturation behavior of two types of PTFE-coated woven glass fiber fabrics is examined and compared to the recently reported saturation behavior of a PVC-coated polyester fabric. With the help of the saturation test data, an extrapolation function is developed that facilitates an estimation of late cycle stiffness behavior based on measured early cycle behavior. Furthermore, the considerable impact of late cycle properties on structural analyses is shown exemplarily in the numerical simulation of a prestressed fabric structure by comparing results achieved from late and early load cycle stiffness parameters.

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“…In the formulation of the implemented polyconvex orthotropic term, unlike the typical multiplicative non-polyconvex ones [ 23 , 26 ], the notion of anisotropic metric tensor

Section: Elastic Materials Models For Textile Membranes and Parametmentioning

confidence: 99%

The Elastic Share of Inelastic Stress–Strain Paths of Woven Fabrics

et al. 2020

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“…However conventional membrane analysis that do not include any wrinkling algorithm lead to an unreal final configuration due to the presence of compression stresses. Ziegler (2001) and Raible (2003) Also in Fig. 3.46 control points M, A and B are given for comparison purposes.…”

Section: Inflation Of a Parachutementioning

confidence: 99%

“…In order to avoid compression stresses, membranes are prestressed. Levy and Spillers (1995), Raible (2003) and Gil (2003) use a prestressed method to analyze membranes which are initially flat in the Euclidean space. An approach that include curved pre-stressed membranes using a projection scheme can be found in Bletzinger and Wüchner (2001).…”

Section: Introductionmentioning

confidence: 99%

“…In the present work, analysis of initially curved pre-stressed membranes is performed using the fiber orientation strategy, which is an extension of the work of Valdés et al (2004). Also the fiber orientation allow to analyze orthotropic membranes, where other possibilities are studied in Raible (2003) and Wüchner and Bletzinger (2005).…”

Section: Introductionmentioning

confidence: 99%

“…Another approach similar to the second one, decompose the strain tensor in its principal directions and then using a new variable, the second principal direction is modified until the compression stresses disappear. In the works of Raible (2003) and Löhnert et al (2003) this approach is used, where explicit formulas for the internal forces are derived.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Analysis of Orthotropic Membrane and Shell Structures Including Fluid-Structure Interaction.

Valdés Vázquez

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Problemas de interacciónn fluido-estructura representan hoy en día un gran desafío en diferentes áreas de ingeniería y ciencias aplicadas. Dentro de las aplicaciones en ingeniería civil, el flujo del viento y los movimientos estructurales pueden ocasionar inestabilidades aeroelásticas en construcciones tales como puentes de gran luz, rascacielos y cubiertas estructurales ligeras. Por otro lado, aplicaciones en biomecánica están interesadas en el estudio de hemodinámica, por ejemplo: flujo sanguíneo en arterias, donde grandes deformaciones de las venas interactúan con fluidos.En la parte estructural de este trabajo, una nueva metodología para el análisis geométricamente no-lineal ortótropo de membranas y láminas sin grados de libertad de rotación es desarrollada basándose en la orientación de la fibra principal del material. Una consecuencia directa de la estrategia de orientación de fibras es la posibilidad de analizar membranas y láminas pretensadas cuya configuración inicial está fuera del plano. Por otra parte, ya que la teoría convencional de membranas permite que existan tensiones de compresión, un modelo de arrugado basado en la modificación de la ecuación constitutiva se presenta. El desarrollo estructural es modelado con elementos finitos provenientes de las ecuaciones de la elastodinámica. La parte de fluidos de este trabajo está gobernada por las ecuaciones de Navier- Stokes para flujos incompresibles, las cuales son modeladas por interpolaciones estabilizadas de elementos finitos. Ya que la solución monolítica de dichas ecuaciones tiene la desventaja que consumen mucho tiempo en la solución de grandes sistemas de ecuaciones, el método de pasos fraccionados se usa para aprovechar las ventajas computacionales que brinda gracias al desacoplamiento de la presión del campo de las velocidades. Además, el esquema α-generalizado para integración en el tiempo para fluidos es adaptado para que se use con la t´ecnica de los pasos fraccionados. El problema de interacción fluido-estructura es formulado como un sistema de tres campos: la estructura, el fluido y el movimiento de la malla. El movimiento del dominio del fluido es tomado en cuenta mediante la formulación arbitraria Lagrangiana-Euleriana, para la cual se usan dos estrategias de movimiento de malla. Para el acoplamiento entre el fluido y la estructura se usa un acoplamiento fuerte por bloques usando la técnica de Gauss-Seidel. Debido a que la interacción entre el fluido y la estructura es altamente no-lineal, se implementa el método de relajación basado en la técnica de Aitken, la cual acelera la convergencia del problema. Finalmente varios problemas se presentan en los diferentes campos, los cuales verifican la eficiencia de los algoritmos implementados. Nowadays, fluid-structure interaction problems are a great challenge of different fields in engineering and applied sciences. In civil engineering applications, wind flow and structural motion may lead to aeroelastic instabilities on constructions such as long-span bridges, high-rise buildings and light-weight roof structures. On the other hand, biomechanical applications are interested in the study of hemodynamics, i.e. blood flow through large arteries, where large structural membrane deformations interact with incompressible fluids. In the structural part of this work, a new methodology for the analysis of geometrically nonlinear orthotropic membrane and rotation-free shell elements is developed based on the principal fiber orientation of the material. A direct consequence of the fiber orientation strategy is the possibility to analyze initially out-ofplane prestressed membrane and shell structures. Additionally, since conventional membrane theory allows compression stresses, a wrinkling algorithm based on modifying the constitutive equation is presented. The structure is modeled with finite elements emerging from the governing equations of elastodynamics. The fluid portion of this work is governed by the incompressible Navier-Stokes equations, which are modeled by stabilized equal-order interpolation finite elements. Since the monolithic solution for these equations has the disadvantage that take great computer effort to solve large algebraic system of equations, the fractional step methodology is used to take advantage of the computational efficiency given by the uncoupling of the pressure from the velocity field. In addition, the generalized-α time integration scheme for fluids is adapted to be used with the fractional step technique. The fluid-structure interaction problem is formulated as a three-field system: the structure, the fluid and the moving fluid mesh solver. Motion of the fluid domain is accounted for with the arbitrary Lagrangian-Eulerian formulation with two different mesh update strategies. The coupling between the fluid and the structure is performed with the strong coupling block Gauss-Seidel partitioned technique. Since the fluid-structure interaction problem is highly nonlinear, a relaxation technique based on Aitken's method is implemented in the strong coupling formulation to accelerate the convergence. Finally several example problems are presented in each field to verify the robustness and efficiency of the overall algorithm, many of them validated with reference solutions.

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