Recommended Finite Element Formulations for the Analysis of Offshore Blast Walls in an Explosion

Many flexible multibody applications are characterized by high inertia forces and motion discontinuities. Because of these characteristics, problems can be encountered when large displacement finite element formulations are used in the simulation of flexible multibody systems. In this investigation, the performance of two different large displacement finite element formulations in the analysis of flexible multibody systems is investigated. These are the incremental corotational procedure proposed in an earlier article (Rankin, C. C., and Brogan, F. A., 1986, ASME J. Pressure Vessel Technol., 108, pp. 165–174) and the non-incremental absolute nodal coordinate formulation recently proposed (Shabana, A. A., 1998, Dynamics of Multibody Systems, 2nd ed., Cambridge University Press, Cambridge). It is demonstrated in this investigation that the limitation resulting from the use of the infinitesmal nodal rotations in the incremental corotational procedure can lead to simulation problems even when simple flexible multibody applications are considered. The absolute nodal coordinate formulation, on the other hand, does not employ infinitesimal or finite rotation coordinates and leads to a constant mass matrix. Despite the fact that the absolute nodal coordinate formulation leads to a non-linear expression for the elastic forces, the results presented in this study, surprisingly, demonstrate that such a formulation is efficient in static problems as compared to the incremental corotational procedure. The excellent performance of the absolute nodal coordinate formulation in static and dynamic problems can be attributed to the fact that such a formulation does not employ rotations and leads to exact representation of the rigid body motion of the finite element. [S1050-0472(00)00604-8]

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Thermomechanical Analysis of the Welding Process Using the Finite Element Method

Journal of Pressure Vessel Technology ◽

10.1115/1.3454296 ◽

1975 ◽

Vol 97 (3) ◽

pp. 206-213 ◽

Cited By ~ 179

Author(s):

E. Friedman

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Welding Process ◽

Thermomechanical Analysis ◽

Analytical Models ◽

The Finite Element Method ◽

Nonuniform Temperature ◽

Butt Weld ◽

Transverse Bending ◽

Finite Element Formulations

Analytical models are developed for calculating temperatures, stresses and distortions resulting from the welding process. The models are implemented in finite element formulations and applied to a longitudinal butt weld. Nonuniform temperature transients are shown to result in the characteristic transverse bending distortions. Residual stresses are greatest in the weld metal and heat-affected zones, while the accumulated plastic strain is maximum at the interface of these two zones on the underside of the weldment.

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Penalty Method Involving Electric Sliding Contact Problem

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.701-702.246 ◽

2014 ◽

Vol 701-702 ◽

pp. 246-249

Author(s):

Sai Tan ◽

Jun Yong Lu ◽

Xin Lin Long ◽

Xiao Zhang

Keyword(s):

Finite Element ◽

Contact Problem ◽

Physical Quantity ◽

Penalty Method ◽

Sliding Contact ◽

Interface Condition ◽

Calculation Results ◽

Coupled Equation ◽

Finite Element Formulations ◽

Methods Numerical

Basing on governing Maxwell and energy equation of rail gun considering armature movement in two dimension, The total domain to be solved is divided into two subdomains: moving (armature) part and static (rail) part, finite element formulations of two subdomains are built independently, then using the interface condition of two subdomains, formulations are connected by coupled equation which is derived out by penalty method. Shifted physical quantity is used to simulate movement. The final magnetic-thermal coupled fields finite element formulations of rail gun are established by these methods. Numerical calculation results compared by theoretical and other numerical results verify that penalty method is an effective way to deal with electric sliding contact problem associating with Shifted physical quantity method.

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A theoretical and numerical comparison of three finite strain finite element formulations for elastic-viscoplastic materials

Computers & Structures ◽

10.1016/0045-7949(83)90162-1 ◽

1983 ◽

Vol 16 (1-4) ◽

pp. 215-222 ◽

Cited By ~ 1

Author(s):

R.A. LeMaster

Keyword(s):

Finite Element ◽

Finite Strain ◽

Numerical Comparison ◽

Finite Element Formulations

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Macro Modeling of Reactive Infiltration Using Level Set Finite Element Formulations

10.1115/imece2000-1239 ◽

2000 ◽

Author(s):

Dinesh Balagangadhar ◽

Gopalaswamy Rajesh

Keyword(s):

Finite Element ◽

Porous Medium ◽

Level Set ◽

Transfer Problem ◽

Ceramic Matrix Composites ◽

Element Formulation ◽

Reactive Infiltration ◽

Macro Modeling ◽

Infiltration Front ◽

Finite Element Formulations

Abstract The process of reactive melt infiltration can be used to fabricate ceramics and ceramic matrix composites. This process involves a liquid metal being allowed to infiltrate a medium with which the liquid reacts to form a resultant ‘matrix’ along with the already present reinforcing fibers. The authors’ previous work on this area revealed that the transient porosity and permeability of a porous medium can be determined for certain geometries from the reaction kinetics and coupled heat and mass transfer problem occurring at the pore level. But the formulation at the macro level, which is essential to optimize the process, has been limited. Towards this end, this paper solves the macro reactive flow problem in a porous medium analytically as well as numerically. The focus of this article will be on the solutions for the advance (displacement) of the ‘infiltration front’ with progressive chemical reaction occurring between the medium and the infiltrant. A finite element formulation is used to solve the problem computationally; a level set formulation is used to track the infiltration front during the process. Excellent agreement is obtained between the analytical and computational solutions thereby validating the level set finite element formulations.

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Uniqueness of the Geometric Representation in Large Rotation Finite Element Formulations

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4001909 ◽

2010 ◽

Vol 5 (4) ◽

Cited By ~ 10

Author(s):

Ahmed A. Shabana

Keyword(s):

Finite Element ◽

Finite Elements ◽

Computer Aided Design ◽

Curvature Vector ◽

Space Curve ◽

Body Motion ◽

Large Rotation ◽

Space Curves ◽

Curvature Continuity ◽

Finite Element Formulations

Several finite element formulations used in the analysis of large rotation and large deformation problems employ independent interpolations for the displacement and rotation fields. As explained in this paper, three rotations defined as field variables can be sufficient to define a space curve that represents the element centerline. The frame defined by the rotations can differ from the Frenet frame of the space curve defined by the same rotation field and, therefore, such a rotation-based representation can provide measure of twist shear deformations and captures the rotation of the beam about its axis. However, the space curve defined using the rotation interpolation has a geometry that can significantly differ from the geometry defined by an independent displacement interpolation. Furthermore, the two different space curves defined by the two different interpolations can differ by a rigid body motion. Therefore, in these formulations, the uniqueness of the kinematic representation is an issue unless nonlinear algebraic constraint equations are used to establish relationships between the two independent displacement and rotation interpolations. Nonetheless, significant geometric and kinematic differences between two independent space curves cannot always be reduced by using restoring elastic forces. Because of the nonuniqueness of such a finite element representation, imposing continuity on higher derivatives such as the curvature vector is not straight forward as in the case of the absolute nodal coordinate formulation (ANCF) that defines unique displacement and rotation fields. ANCF finite elements allow for imposing curvature continuity without increasing the order of the interpolation or the number of nodal coordinates, as demonstrated in this paper. Furthermore, the relationship between ANCF finite elements and the B-spline representation used in computational geometry can be established, allowing for a straight forward integration of computer aided design and analysis.

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