Improved Procedures for Static and Dynamic Analyses of Wrinkled Membranes

2006 ◽  
Vol 74 (3) ◽  
pp. 590-594 ◽  
Author(s):  
Amit Shaw ◽  
D Roy
Keyword(s):  
Deformation Gradient ◽  
Membrane Structures ◽  
Principal Stresses ◽  
Flexible Membrane ◽  
Integration Schemes ◽  
Present Context ◽  
Finite Element Procedure ◽  
Tension Field Theory ◽  
Dynamic Excitations ◽  
Better Than

An analysis of large deformations of flexible membrane structures within the tension field theory is considered. A modification of the finite element procedure by Roddeman et al. (Roddeman, D. G., Drukker, J., Oomens, C. W. J., Janssen, J. D., 1987, ASME J. Appl. Mech. 54, pp. 884–892) is proposed to study the wrinkling behavior of a membrane element. The state of stress in the element is determined through a modified deformation gradient corresponding to a fictive nonwrinkled surface. The new model uses a continuously modified deformation gradient to capture the location orientation of wrinkles more precisely. It is argued that the fictive nonwrinkled surface may be looked upon as an everywhere-taut surface in the limit as the minor (tensile) principal stresses over the wrinkled portions go to zero. Accordingly, the modified deformation gradient is thought of as the limit of a sequence of everywhere-differentiable tensors. Under dynamic excitations, the governing equations are weakly projected to arrive at a system of nonlinear ordinary differential equations that is solved using different integration schemes. It is concluded that implicit integrators work much better than explicit ones in the present context.

scholarly journals A Finite Element Model for the Analysis of Wrinkled Membrane Structures

2003 ◽  
Vol 18 (1) ◽  
pp. 1-14 ◽  
Author(s):  
René Ziegler ◽  
Werner Wagner ◽  
Kai-Uwe Bletzinger
Keyword(s):  
Finite Element ◽  
Quadratic Convergence ◽  
Element Model ◽  
Significant Progress ◽  
Membrane Structures ◽  
Wrinkling Analysis ◽  
Convergence Behaviour ◽  
Consistent Linearization ◽  
Wrinkled Membrane ◽  
Tension Field Theory

The problem of wrinkling in membrane structures has been a field of research since the publication of the tension field theory for plane structures. Significant progress in wrinkling analysis of arbitrarily shaped membranes has been made with the development of numerical methods. In the paper we present the enhancements of a standard finite element membrane formulation which allow to depict the wrinkles within the plane of the structure. A mathematical-numerical method is derived, which describes a valid stress state by minimising the differences in the stress density function while observing the wrinkling conditions. A consistent linearization of the proposed algorithms ensures quadratic convergence behaviour.

scholarly journals On the Integration Schemes of Retrieving Impulse Response Functions from Transfer Functions

2010 ◽  
Vol 2010 ◽  
pp. 1-9 ◽  
Author(s):  
Kui Fu Chen ◽  
Yan Feng Li
Keyword(s):  
Numerical Integration ◽  
Transfer Functions ◽  
Sampling Interval ◽  
High Order ◽  
Impulse Response Functions ◽  
Inverse Laplace Transformation ◽  
High Order Scheme ◽  
Integration Schemes ◽  
Order Scheme ◽  
Better Than

The numerical inverse Laplace transformation (NILM) makes use of numerical integration. Generally, a high-order scheme of numerical integration renders high accuracy. However, surprisingly, this is not true for the NILM to the transfer function. Numerical examples show that the performance of higher-order schemes is no better than that of the trapezoidal scheme. In particular, the solutions from high-order scheme deviate from the exact one markedly over the rear portion of the period of interest. The underlying essence is examined. The deviation can be reduced by decreasing the frequency-sampling interval.

Grindability Evaluation of Advanced Ceramics

2004 ◽  
Vol 471-472 ◽  
pp. 132-135 ◽  
Author(s):  
Ai Bing Yu ◽  
L.J. Zhong ◽  
Xin Li Tian
Keyword(s):  
Evaluation System ◽  
Comprehensive Evaluation ◽  
Fuzzy Comprehensive Evaluation ◽  
Experimental Results ◽  
Fuzzy Evaluation ◽  
Grinding Forces ◽  
Principal Stresses ◽  
Advanced Ceramics ◽  
Evaluation Theory ◽  
Better Than

Evaluation system of grindability was proposed for advanced ceramics. Grinding forces and material removals of SiC, Al2O3, Si3N4 and ZrO2 were measured. Grindabilities of ceramics were evaluated with property parameters based on fuzzy comprehensive evaluation theory. The experimental results suggest that grindabilities of SiC and Al2O3 are better than those of Si3N4 and ZrO2. The fuzzy evaluation results show grindabilities of SiC and Al2O3 ceramics are classified as grade of very easy to grind, and Si3N4 and ZrO2 are classified as grade of difficult to grind. The ranking of maximum grinding principal stresses of ceramics considering Poisson’s ratio is SiC, Al2O3, ZrO2 and Si3N4. Theoretical analysis calculated with property parameters is consistent with experimental results in comparison of grinding output parameters. The proposed evaluation system for ceramic grindability is feasible, and the evaluated results are comprehensive and reasonable.

scholarly journals Boundary shape design of planar membrane structures based on an airy stress model

2020 ◽  
Vol 12 (4) ◽  
pp. 168781402091603
Author(s):  
Mingjun Liu
Keyword(s):  
Stress Field ◽  
Membrane Structure ◽  
Shape Design ◽  
Stress Model ◽  
Membrane Structures ◽  
Principal Stresses ◽  
Accurate Analysis ◽  
Simple Method ◽  
Edge Structure ◽  
Stress Simulation

Maintaining surface accuracy is crucial to realizing the required performance of membrane structure. However, compressive stress inevitably leads to wrinkling, and the accurate analysis of the stresses becomes significant. The present study analyzed membrane structures with discrete loads. First, a simple method was proposed and the stress field was accurately described using an Airy stress model. The first and second principal stresses were obtained, and regions of wrinkling with negative stress were predicted. Second, for a square membrane structure, vertical tensions around the boundary were applied such that in-plane stresses were more evenly distributed. Finally, to reduce the wrinkling areas more effectively, an arc-edge structure was designed by removing some areas of low-stress. Simulation results showed that the in-plane stress field distribution was described accurately and the wrinkling regions were diminished effectively with the proposed method.

Experimental determination of wind pressure distribution for cylindrical and spherical flexible membrane structures

1995 ◽  
Vol 22 (1) ◽  
pp. 23-31 ◽  
Author(s):  
N. K. Srivastava ◽  
N. Turkkan
Keyword(s):  
Pressure Distribution ◽  
Flexible Structures ◽  
Experimental Studies ◽  
Wind Pressure ◽  
Support Pressure ◽  
Membrane Structures ◽  
Flexible Membrane ◽  
Internal Support ◽  
Wind Tunnel Study

Wind interaction with flexible structures, such as air-supported structures, is different from that of the standard rigid structures. Very few experimental studies are available in the literature with regards to wind effects on such structures. This paper presents an experimental wind tunnel study on hemispherical and cylindrical models of varying ratios of height to base width. The results of the steady state pressure distribution on flexible air-supported models are compared with those of the rigid models, which are generally known. Other varying parameters are also considered, such as wind velocity and direction, internal support pressure, and the Reynolds number. Key words: structure, experimental, wind pressure distribution, flexible membrane, cylindrical, spherical.

Reduced Order Modeling of Deflection of a Membrane Covered Airfoil in a Fluid Flow

2013 ◽  
Author(s):  
Srinath Narayana Murthy ◽  
Jaikumar Loganathan ◽  
Ashok Gopinath
Keyword(s):  
Laplace Equation ◽  
Membrane Surface ◽  
Surface Tension Force ◽  
Radius Of Curvature ◽  
Rigid Object ◽  
Flexible Membrane ◽  
Reduced Order ◽  
Supported Membrane ◽  
Simply Supported ◽  
Better Than

Flow over a flexible membrane is different to that over a rigid object. Fluid stresses developed over a membrane create a deflection, which in turn affects the flow field and generates a new stress distribution, thereby altering the original deflection. The behavior of the membrane can be modeled using the Young-Laplace equation which links the pressure difference across the membrane and the surface tension force with the radius of curvature of the membrane surface. In this work a computational approach is developed to solve the Young-Laplace equation. The approach is validated with a simple case of simply supported membrane subjected to a pressure load and a pretension. The performance of a S825 airfoil whose upper surface is replaced with a membrane is studied for various angles of attack. It is noted that the deformed airfoils perform better than the S825 till α = 6°. Beyond this angle of attack it is observed that the drop in performance is small.

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