Highly efficient solid and solid-shell finite elements with mixed strain–displacement assumptions specifically set up for explicit dynamic simulations using symbolic programming

Mattern, Steffen; Schmied, Christoph; Schweizerhof, Karl

doi:10.1016/j.compstruc.2015.03.009

Cited by 9 publications

(8 citation statements)

References 29 publications

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“…In this example, the response of the developed CPE and other element formulations under bending deformation mode is tested [Mattern et al (2015)]. To this end, a cube with an edge length of L = 1.0 [m] is considered, which is subjected to one set of four forces on the nodes of the surface X 1 = 0 causing a bending moment about the positive direction e 3 and another set of four forces on the nodes of the surface X 1 = L causing a bending moment about the negative direction e 3 (see Fig.…”

Section: Cube Under Bendingmentioning

confidence: 99%

The Cosserat Point Element as an Accurate and Robust Finite Element Formulation for Implicit Dynamic Simulations

Jabareen

Pestes

2019

Int. J. Comput. Methods

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The reliability of numerical simulations manifested the need for an accurate and robust finite element formulation. Therefore, in the present study, an eight node brick Cosserat point element ( CPE ) for the nonlinear dynamic analysis of three-dimensional (3D) solids including both thick and thin structures is developed. Within the present finite element formulation, a strain energy function is proposed and additively decoupled into two parts. One part is characterized by any 3D strain energy function, while the other part controls the response to inhomogeneous deformations. Several example problems are presented, which demonstrate the accuracy and the robustness of the developed CPE in modeling the dynamic response of elastic structures.

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Section: Cube Under Bendingmentioning

confidence: 99%

The Cosserat Point Element as an Accurate and Robust Finite Element Formulation for Implicit Dynamic Simulations

Jabareen

Pestes

2019

Int. J. Comput. Methods

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“…The underdevelopment of solid-shell elements in the field of sheet metal forming may result from the technology adopted in the element formulation. As claimed in [17], there are only a few contributions using EAS in combination with explicit time integration. The EAS is based on the introduction of additional degrees of freedom at the element level, which can be condensed using local equation calculation and leads to exactly accurate element formulations in the context of implicit time integration methods.…”

Section: Introductionmentioning

confidence: 99%

Explicit Analysis of Sheet Metal Forming Processes Using Solid-Shell Elements

Liu

et al. 2021

Metals

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To simulate sheet metal forming processes precisely, an in-house dynamic explicit code was developed to apply a new solid-shell element to sheet metal forming analyses, with a corotational coordinate system utilized to simplify the nonlinearity and to integrate the element with anisotropic constitutive laws. The enhancing parameter of the solid-shell element, implemented to circumvent the volumetric and thickness locking phenomena, was condensed into an explicit form. To avoid the rank deficiency, a modified physical stabilization involving the B-bar method and reconstruction of transverse shear components was adopted. For computational efficiency of the solid-shell element in numerical applications, an adaptive mesh subdivision scheme was developed, with element geometry and contact condition taken as subdivision criteria. To accurately capture the anisotropic behavior of sheet metals, material models with three different anisotropic yield functions were incorporated. Several numerical examples were carried out to validate the accuracy of the proposed element and the efficiency of the adaptive mesh subdivision.

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“…Most of the isogeometric solid‐shell element formulations proposed in the literature do not consider dynamic problems or the implications of using explicit time integration. However, numerous recently published contributions show a great interest in using solid‐shell elements in explicit dynamic simulations, eg, many formulations have been proposed in the context of classical finite elements . Furthermore, explicit metal forming simulations with solid‐shell elements were demonstrated in the works of Li et al and Xu et al Traditionally, bilinearly interpolated shell elements have dominated explicit analyses because using higher‐order shape functions (which are Lagrange polynomials) reduces the stable time‐step size.…”

Section: Introductionmentioning

confidence: 99%

Isogeometric thickness stretchable shell: Efficient formulation for nonlinear dynamic problems

Hokkanen

Pedroso

2019

Numerical Meth Engineering

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An isogeometric shell element with through-thickness stretch is introduced and applied to quasi-static and dynamic problems. The shell element supports full three-dimensional constitutive laws, ie, the plane stress assumption is not required. An updated Lagrangian rate formulation is adopted, and biquadratic spline-based interpolation functions are used for in-plane interpolation. The concept of fiber mass scaling is proposed to lower the highest eigenfrequencies to improve the performance of the formulation. Clamped and unclamped knot vectors are compared, and the advantages of using unclamped knot vectors are demonstrated. The shell element is validated using several benchmark tests, which indicate good performance of the proposed formulation. KEYWORDS explicit dynamics, isogeometric analysis, large deformations, thick-shell element, unclamped knot vectors Recently, the focus in the shell finite element technology has shifted toward more advanced formulations, such as thickness stretchable shell elements and solid shells. Two isogeometric solid-shell elements have been proposed by Hosseini et al 20,21 ; the latter formulation was extended to model propagation of delamination in composite materials. 22 Int J Numer Methods Eng. 2019;119:105-127.wileyonlinelibrary.com/journal/nme

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Highly efficient solid and solid-shell finite elements with mixed strain–displacement assumptions specifically set up for explicit dynamic simulations using symbolic programming

Cited by 9 publications

References 29 publications

The Cosserat Point Element as an Accurate and Robust Finite Element Formulation for Implicit Dynamic Simulations

The Cosserat Point Element as an Accurate and Robust Finite Element Formulation for Implicit Dynamic Simulations

Explicit Analysis of Sheet Metal Forming Processes Using Solid-Shell Elements

Isogeometric thickness stretchable shell: Efficient formulation for nonlinear dynamic problems

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