Large deformation analysis of fully incompressible hyperelastic curved beams

Dadgar‐Rad, Farzam; Sahraee, Shahab

doi:10.1016/j.apm.2020.12.001

Cited by 12 publications

(6 citation statements)

References 36 publications

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“…Recent studies have examined the performance of the developed elements under large rotations by solving this problem using meshes ranging from three up to a hundred of elements. 18,19 The exact solution to this problem is a circular arc with radius R = EI∕M. To deform the rod into a full closed circle, an end moment M = 2𝜋EI∕L needs to be applied.…”

Section: Pure Bending Of a Cantilever Beammentioning

confidence: 99%

“…The first test, serving as a benchmark, deals with a cantilever of length L and bending stiffness

E I

loaded by a concentrated end moment M on its right end. Recent studies have examined the performance of the developed elements under large rotations by solving this problem using meshes ranging from three up to a hundred of elements 18,19 . The exact solution to this problem is a circular arc with radius

R = E I / M

.…”

Section: Numerical Examplesmentioning

confidence: 99%

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Efficient finite difference formulation of a geometrically nonlinear beam element

Jirásek

Ribolla

Horák

2021

Numerical Meth Engineering

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The article is focused on a two-dimensional geometrically nonlinear formulation of a Bernoulli beam element that can accommodate arbitrarily large rotations of cross sections. The formulation is based on the integrated form of equilibrium equations, which are combined with the kinematic equations and generalized material equations, leading to a set of three first-order differential equations. These equations are then discretized by finite differences and the boundary value problem is converted into an initial value problem using a technique inspired by the shooting method. Accuracy of the numerical approximation is conveniently increased by refining the integration scheme on the element level while the number of global degrees of freedom is kept constant, which leads to high computational efficiency. The element has been implemented into an open-source finite element code. Numerical examples show a favorable comparison with standard beam elements formulated in the finite-strain framework and with analytical solutions.

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Section: Pure Bending Of a Cantilever Beammentioning

confidence: 99%

“…The first test, serving as a benchmark, deals with a cantilever of length L and bending stiffness

E I

R = E I / M

.…”

Section: Numerical Examplesmentioning

confidence: 99%

Efficient finite difference formulation of a geometrically nonlinear beam element

Jirásek

Ribolla

Horák

2021

Numerical Meth Engineering

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“…The beam has a length of 4 meters, and the bending stiffness EI of the beam cross-section is assumed to be l. The bending moments applied on the right end are up to 4π, which can make the member wind twice around itself. This is a classical nonlinear structural analysis problem that has been investigated by several researchers [71][72][73][74] during the past decades. Recent studies tried to solve this large-rotation problem using the fine-meshed FEM, where the number of which ranges from three up to a hundred for a single member [71][72], showing the intensive computational expense.…”

Section: Example 1 -Cantilever Beams Under End Momentmentioning

confidence: 99%

Volume 19 Number 4

2023

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The International Journal of Advanced Steel Construction provides a platform for the publication and rapid dissemination of original and up-to-date research and technological developments in steel construction, design and analysis. Scope of research papers published in this journal includes but is not limited to theoretical and experimental research on elements, assemblages, systems, material, design philosophy and codification, standards, fabrication, projects of innovative nature and computer techniques. The journal is specifically tailored to channel the exchange of technological know-how between researchers and practitioners. Contributions from all aspects related to the recent developments of advanced steel construction are welcome.Disclaimer. No responsibility is assumed for any injury and / or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Subscription inquiries and change of address. Address all subscription inquiries and correspondence to Member Records, IJASC. Notify an address change as soon as possible. All communications should include both old and new addresses with zip codes and be accompanied by a mailing label from a recent issue. Allow six weeks for all changes to become effective.

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“…Perform the linearlization procedure to Eqs. ( 6) and ( 7), two non-linear parts for finite deformation analysis are derived (10) where K tan is the tangent stiffness matrix that includes the geometric non-linear and material nonlinear parts of the problem…”

Section: Three-dimensional Finite Element Formulations For Non-linear...mentioning

confidence: 99%

Finite element analysis for three-dimensional hyper-elastic problems

Nguyen,

Huynh,

Nguyen

et al. 2021

Sci. Tech. Dev. J.

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Hyper-elastic materials are special elastic material that the stress can be derived by the strain energy density function. The most attractive property of these rubber-like materials is their ability to undergo large strains with small loads and recover their initial shape after unloading. Hyper-elastic materials are widely used in engineering such as tire, elastomeric bearing pad, belt drives, rail pad and so on. Due to the large strain state in most of application of this type of material, the behavior of hyper-elastic is often considered in finite deformation analysis. In comparison with linear material, analysis for hyper-elastic material which have nonlinearities is more complicated because both material nonlinearity and geometric nonlinearity should be considered. Along with the development of computer and numerical methods, the finite element method (FEM) is known as a powerful numerical computation tool that can helps to solve engineering problems in many fields such as structural, thermal, electronic, and biomedical analyses. Actually, most of practical engineering problems appear in three-dimensional (3D) state, especially in nonlinear analyses. So, the development for an effective numerical method for 3D nonlinear problems is very necessary. In this study, a finite element approach with 8-node hexahedron element is presented for analyses of large deformation problems of hyper-elastic material. The compressible neo-Hookean is used as the constitutive model for 3D hyper-elastic problems and the total Lagrange formulation is applied for the discretization of large deformation problems. To obtain the nonlinear solutions, the standard Newton-Raphson algorithm with constant load step is chosen as the iteration method. The computing programs are built with Matlab language. To verify the accuracy of the present approach, the obtained results are compared with the reference solutions given by Ansys program.

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Large deformation analysis of fully incompressible hyperelastic curved beams

Cited by 12 publications

References 36 publications

Efficient finite difference formulation of a geometrically nonlinear beam element

Efficient finite difference formulation of a geometrically nonlinear beam element

Volume 19 Number 4

Finite element analysis for three-dimensional hyper-elastic problems

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