Arbitrary Lagrangian-Eulerian formulations for cutting pattern generation of tensile membrane structures (original) (raw)
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Finite Elements in Analysis and Design, 2012
The purpose of this paper is to show a practical implementation of a genetic algorithm for minimizing membrane stresses discrepancies between the actual assembled equilibrium and the specified design state. The method prevents the surface wrinkle problems in membrane structures under service loading and determines an optimum cutting pattern, which accounts for the designed stresses of the membrane structures. Using the displacements of the 3-D surface as the key variables, the proposed method utilizes a geometrically nonlinear finite element analysis based upon the improved the stress-adapted numerical form finding of pre-stressed surfaces by the updated reference strategy. The model of genetic algorithm and the genetic operators are then designed to solve numerically the optimization problem. The method is validated through examples and compared with the available data. The analysis results show no significant differences between the assumed designed stresses and the actual stresses in the membrane.
Advanced approaches for analysis and form finding of membrane structures with finite elements
2017
Part I deals with material modelling of woven fabric membranes. Due to their structure of crossed yarns embedded in coating, woven fabric membranes are characterised by a highly nonlinear stress-strain behaviour. In order to determine an accurate structural response of membrane structures, a suitable description of the material behaviour is required. A linear elastic orthotropic model approach, which is current practice, only allows a relative coarse approximation of the material behaviour. The present work focuses on two different material approaches: A first approach becomes evident by focusing on the meso-scale. The inhomogeneous, however periodic structure of woven fabrics motivates for microstructural modelling. An established microstructural model is considered and enhanced with regard to the coating stiffness. Secondly, an anisotropic hyperelastic material model for woven fabric membranes is considered. By performing inverse processes of parameter identification, fits of the two different material models w.r.t. measured data from a common biaxial test are shown. The results of the inversely parametrised material models are compared and discussed. Part II presents an extended approach for a simultaneous form finding and cutting patterning computation of membrane structures. The approach is formulated as an optimisation problem in which both the geometries of the equilibrium and cutting patterning configuration are initially unknown. The design objectives are minimum deviations from prescribed stresses in warp and fill direction along with minimum shear deformation. The equilibrium equations are introduced into the optimisation problem as constraints. Additional design criteria can be formulated (for the geometry of seam lines etc.
Surface Fitting Approach for Tensile Membranes Design
2004
The aim of this paper is to introduce a method for the conceptual design of membrane structures. Actually, there is a lack of computer based tools for the people involved in these first stages of the design process, in which the shape of the membrane is being defined. Not many parameters are needed at this stage for the designer. An easy graphic interface is needed, in which the designer had the possibility of varying in real time the shape of the membrane, and the environment around it, to achieve the desired shapes. A hybrid algorithm, based on a structural analysis and a surface fitting approach has been carried out to meet all the requirements.
Thin Sheet Forming Numerical Analysis with a Membrane Approach
Modelling of Metal Forming Processes, 1988
A numerical model for solving either elastic-plastic, elastic-viscoplastic or purely viscoplastic deformation of thin sheets is presented using a membrane mechanical approach.The Finite Element Method is used associated with an incremental updated Lagrangian procedure.The mechanical equations are the principle of virtual work written in terms of plane stress at the end of each increment and an incremental implicit flow rule obtained by the time integration of the constitutive relations over the increment.The examples given here are the computation of hemispherical punch stretching for the elastic-plastic behavior and the application to superplastic forming with the viscoplastic flow rule.
THE RELATIONSHIP BETWEEN GEOMETRY AND OPTIMIZATION IN STRUCTURAL MEMBRANE DESIGN
The system formed in today’s architecture by the membrane material which has a light structure and is more affordable compared to other materials, is defined by qualities such as textile architecture, flexible architecture and portable architecture. Nevertheless, as a result of searches for a reusable, recyclable and resolvable material in the nature, new materials and construction systems are being created resources on design process. The achieved level in material technologies, moving material performances to upper levels and the increase in textile composites have enabled structural membranes to be used in long-span systems more frequently in this process. Structural membrane is lighter, more affordable, replaceable or self-cleaning material when it gets dirty, and it can easily take the desired geometrical shape. As a structural material of membrane; increases performances of steel, wood etc. and create whole structure together. Form finding in membrane structures, related with balanced under loads. In this study, relationship between geometric models (catenary, minimal surface) and optimization metods (force density, dynamic relaxation) will evualate.
Industrial Design and Analysis of Structural Membranes
International Journal of Space Structures, 2009
This overview paper summarizes the status of design and analysis of small and large, complex, flexible and adaptable industrial membrane structures in architecture, automotive and space industries, with the numerical tools developed and implemented by the authors and their affiliations. Examples from aero-space membranes, airbag simulations used by car makers, and from impact biomechanics, enlarge the field of application beyond structural engineering.
An Eulerian Finite Element Model of the Metal Cutting Process
The Eulerian element formulation was employed in the modeling of the orthogonal metal cutting process of commercial purity copper. The constitutive material models elastic-plastic hydrodynamic and Johnson-Cook, were utilized in modeling the workpiece behavior. The capabilities of each model to replicate the experimental chip geometry, stress and strain distributions, and cutting forces, were investigated. The numerical strain distributions, were in good agreement with the experimental strain distribution. The maximum strains of p ε = 8.3 and p ε = 5.6 for the Johnson-Cook material and hydrodynamic material, respectively, occurred in the tool tip region, and were in good correlation with the experimental strain of p ε = 8.1 at this location. The experimental and numerical distributions, all predicted strains of approximately p ε = 3.5 to 3.6 beneath the machined surface and adjacent to the rake face. The stress distributions in both of the investigated materials were noticeable different. The Johnson-Cook model showed a stress increase of up to 425 MPa in the primary deformation zone, while the hydrodynamic model predicted increased stresses of 380 MPa in the secondary deformation zone. The hydrodynamic stress distribution was more consistent with experimental findings, which similarly showed a stress increase, up to 360 MPa, in the secondary deformation zone. The maximum stress in the hydrodynamic material (410 MPa) and in the Johnson-Cook material (438 MPa) were located at the tool tip, and showed good correlation to the maximum experimental stress of 422 MPa, also occurring at the tool tip. The sizes of both the primary deformation zone (350 µm), and the secondary deformation zone (50 µm) predicted by the hydrodynamic and Johnson-Cook material models were in agreement with the experimental observations. The steady state cutting force prediction of the hydrodynamic material was 1332 N, and was within 13% of the experimental findings. The numerical–experimental correlations indicate the Eulerian finite element approach is an effective way of modeling the metal cutting process.
Formulation of a new finite element based on assumed strains for membrane structures
International Journal of Advanced Structural Engineering, 2019
In this paper, a new triangular membrane finite element with in-plane drilling rotation has been developed using the strain-based approach for static and free vibration analyses. The proposed element, having three degrees of freedom at each of the three corner nodes, is based on assumed strain functions satisfying both compatibility and equilibrium equations. Numerical investigations have been conducted using several tests, including static and free vibration problems, and the obtained results are compared with analytical and numerical available solutions. It is found that efficient convergence characteristics and accurate results can be achieved using the developed element.
Membrane triangles with corner drilling freedoms. I - The EFF element
Finite Elements in Analysis and Design, 1992
The formulation of 3-node 9-DOF membrane elements with normal-to-element-plane rotations (drilling freedoms) is examined in the context of parametrized variational principles. In particular, attention is given to the application of the extended free formulation (EFF) to the construction of a triangular membrane element with drilling freedoms that initially has complete quadratic polynomial expansions in each displacement component. The main advantage of the EFF over the free formulation triangle is that an explicit form is obtained for the higher-order stiffness.