Influence of the Subtended Angle on the Behavior of Folded Tape Springs

2018 ◽  
Author(s):  
Marinus G. de Jong ◽  
Werner W. P. J. van de Sande ◽  
Just L. Herder
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Strain Energy ◽  
Element Model ◽  
Constant Cross Section ◽  
Curvature Analysis ◽  
Thin Walled Structures ◽  
Constant Radius ◽  
Thin Walled ◽  
Force Generator

Tape springs are thin-walled structures with zero longitudinal and constant transverse curvature. Folding them twice and connecting both ends creates a tape loop which acts as a linear guide. When using a tape spring with a non-constant cross-section, a force generator can be created. At this time there is insufficient understanding of the influence of the tape spring’s cross-section on its behavior. This study investigates the influence of the subtended angle on the tape spring’s behavior, especially the energy distribution and the fold radius. A tape spring is once folded in a finite element model. By performing a curvature analysis of this folded geometry, the different regions within a tape spring are identified. This information is used to identify the amount of strain energy of each region. Finally, the fold radius and fold angle are determined by analyzing the geometry of the bent region. The analysis showed that the energy within the transition regions cannot be neglected. The energy within these regions as ratio of the total energy and the length of the transition regions both increase with the subtended angle. It is also shown that the fold radius is not constant when the subtended angle is small. Therefore, when designing a force generator using tape loops, the energy within the transition regions should be taken into account. The subtended angle should not be small to ensure a constant radius.

Properties of Twofold Tape Loops: The Influence of the Subtended Angle

2019 ◽  
Vol 11 (2) ◽  
Author(s):  
Marinus G. de Jong ◽  
Werner W. P. J. van de Sande ◽  
Just L. Herder
Keyword(s):  
Energy Distribution ◽  
Cross Section ◽  
Energy State ◽  
Linear Guide ◽  
Curvature Analysis ◽  
Transverse Curvature ◽  
Thin Walled Structures ◽  
Constant Radius ◽  
Thin Walled ◽  
Key Aspects

Tape springs are thin-walled structures with zero longitudinal and constant transverse curvature. Folding them twice and connecting both ends creates a tape loop which acts as a linear guide. At this time, there is insufficient understanding of the influence of the tape spring's cross section on its behavior. This study investigates the influence of the subtended angle on the tape spring's behavior, especially the energy distribution and the fold radius. First, some key aspects in the design of a twofold tape loop are discussed. By performing a curvature analysis of this folded geometry, the different regions within a tape spring are identified. This information is used to identify the influence of the subtended angle on the geometry and energy state of the tape loop. The fold radius and fold angle are determined by analyzing the geometry of the fold region. The analysis showed that the energy within the transition regions cannot be neglected. The energy within these regions and the length of the transition regions both increase with the subtended angle. It is also shown that the fold radius is not constant when the subtended angle is small. The subtended angle should be above 100 deg to ensure a constant radius.

scholarly journals Dynamic Analysis of Tapered Thin-Walled Beams Using Spectral Finite Element Method

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Yiping Shen ◽  
Zhijun Zhu ◽  
Songlai Wang ◽  
Gang Wang
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Wind Turbine ◽  
Element Model ◽  
Rotor Blades ◽  
Mode Shapes ◽  
Modal Frequency ◽  
Thin Walled Structures ◽  
Thin Walled ◽  
Spectral Finite Element

Tapered thin-walled structures have been widely used in wind turbine and rotor blade. In this paper, a spectral finite element model is developed to investigate tapered thin-walled beam structures, in which torsion related warping effect is included. First, a set of fully coupled governing equations are derived using Hamilton’s principle to account for axial, bending, and torsion motion. Then, the differential transform method (DTM) is applied to obtain the semianalytical solutions in order to formulate the spectral finite element. Finally, numerical simulations are conducted for tapered thin-walled wind turbine rotor blades and validated by the ANSYS. Modal frequency results agree well with the ANSYS predictions, in which approximate 30,000 shell elements were used. In the SFEM, one single spectral finite element is needed to perform such calculations because the interpolation functions are deduced from the exact semianalytical solutions. Coupled axial-bending-torsion mode shapes are obtained as well. In summary, the proposed spectral finite element model is able to accurately and efficiently to perform the modal analysis for tapered thin-walled rotor blades. These modal frequency and mode shape results are important to carry out design and performance evaluation of the tapered thin-walled structures.

Support-Condition Analyses of Rotating Beams Under Distributed Imbalance Loading

2011 ◽  
Author(s):  
Kai Jokinen ◽  
Erno Keskinen ◽  
Marko Jorkama ◽  
Wolfgang Seemann
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Cross Section ◽  
Cross Sections ◽  
Natural Frequencies ◽  
Element Model ◽  
Mode Shapes ◽  
Constant Cross Section ◽  
Support Condition ◽  
Beam Elements

In roll balancing the behaviour of the roll can be studied either experimentally with trial weights or, if the roll dimensions are known, analytically by forming a model of the roll to solve response to imbalance. Essential focus in roll balancing is to find the correct amount and placing for the balancing mass or masses. If this selection is done analytically the roll model used in calculations has significant effect to the balancing result. In this paper three different analytic methods are compared. In first method the mode shapes of the roll are defined piece wisely. The roll is divided in to five parts having different cross sections, two shafts, two roll ends and a shell tube of the roll. Two boundary conditions are found for both supports of the roll and four combining equations are written to the interfaces of different roll parts. Totally 20 equations are established to solve the natural frequencies and to form the mode shapes of the non-uniform roll. In second model the flexibility of shafts and the stiffness of the roll ends are added to the support stiffness as serial springs and the roll is modelled as a one flexibly supported beam having constant cross section. Finally the responses to imbalance of previous models are compared to finite element model using beam elements. Benefits and limitations of each three model are then discussed.

scholarly journals Simplified Analytical Model for Predicting Neutral Cross-Section Position of Lenticular Deployable Composite Boom in Tensile Deformation

Materials ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 7809
Author(s):  
Li-Wu Wang ◽  
Jiang-Bo Bai ◽  
Yan Shi
Keyword(s):  
Finite Element ◽  
Theoretical Model ◽  
Cross Section ◽  
Tensile Deformation ◽  
Three Dimensional ◽  
Element Model ◽  
Thin Walled Structures ◽  
Deformation Ability ◽  
Rigid Rod ◽  
Neutral Cross Section

Foldable and deployable flexible composite thin-walled structures have the characteristics of light weight, excellent mechanical properties and large deformation ability, which means they have good application prospects in the aerospace field. In this paper, a simplified theoretical model for predicting the position of the neutral section of a lenticular deployable composite boom (DCB) in tensile deformation is proposed. The three-dimensional lenticular DCB is simplified as a two-dimensional spring system and a rigid rod, distributed in parallel along the length direction. The position of the neutral cross-section can be determined by solving the balance equations and geometric relations. In order to verify the validity of the theoretical model, a finite element model of the tensile deformation of a lenticular DCB was established. The theoretical prediction results were compared with the finite element calculation results, and the two results were in good agreement.

scholarly journals Numerical Models of the Connection of Thin-Walled Z-Profile Roof Purlins

Materials ◽  
2021 ◽  
Vol 14 (21) ◽  
pp. 6573
Author(s):  
Přemysl Pařenica ◽  
Petr Lehner ◽  
Jiří Brožovský ◽  
Martin Krejsa
Keyword(s):  
Cross Section ◽  
Numerical Models ◽  
Element Model ◽  
Cross Sectional ◽  
Physical Test ◽  
Thin Walled Structures ◽  
Practical Design ◽  
Thin Walled ◽  
Bolt Connection ◽  
Experimental Preparation

High thin-walled purlins of Z cross-section are important elements in steel wide-span structures. Their behaviour is influenced by many variables that need to be examined for every specific case. Their practical design thus requires extended knowledge of their behaviour for the possible configurations and dimensions. Numerical analysis verified by experimental investigation can thus enrich such knowledge. Numerical models have the advantage of repeatability and the ability to offer parametric changes. The parametric study presented shows a detailed description of a finite element model of thin-walled cross-sectional roof purlins connected to other roof elements. Models include various approaches to modelling bolt connection. Two schemes of purlins, with and without cleats, are presented. The results of different approaches in numerical modelling are compared with the results of a physical test on a real structure. The article shows a significant agreement in the case of specific approaches and points out the differences with others. The results can be helpful in terms of how to approach the modelling of thin-walled structures and the effective approach to experimental preparation.

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