An efficient reduced computational method for nonlinear homogenization problems: the Hashin–Shtrikman type Finite Element method (HSFE)

PAMM ◽  
2018 ◽  
Vol 18 (1) ◽  
Author(s):  
Fabiola Cavaliere ◽  
Stephan Wulfinghoff ◽  
Stefanie Reese
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Computational Method ◽  
Homogenization Problems ◽  
Nonlinear Homogenization ◽  
Element Method

Development of Bifurcation Analysis Method for Rate Dependent Materials

2019 ◽  
Vol 794 ◽  
pp. 220-225
Author(s):  
Daiki Towata ◽  
Yuichi Tadano
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Bifurcation Analysis ◽  
Stiffness Matrix ◽  
Computational Method ◽  
Analysis Method ◽  
The Finite Element Method ◽  
Tangent Stiffness Matrix ◽  
Rate Dependent ◽  
Element Method

In this study, a novel numerical method to analyze the bifurcation problemof a rate dependent material using the finite element method is proposed. The consistent stiffness matrix, which is required for a bifurcation analysis using the finite element method, for a rate dependent material is generally hard to compute, therefore, a computational method to calculate the tangent stiffness matrix based on a numerical differential is introduced so that exact bifurcation analyses for the rate dependent material can be conducted. A numerical example of the proposed method is demonstrated, and the adequacy of the proposed method is discussed.

A Finite Element Method-Based Potential Theory Approach for Optimal Ice Routing

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Henry Piehl ◽  
Aleksandar-Saša Milaković ◽  
Sören Ehlers
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fuel Consumption ◽  
Computational Method ◽  
Ice Thickness ◽  
Test Problems ◽  
Theory Approach ◽  
Optimal Route ◽  
Cost Information ◽  
Element Method

Shipping in ice-covered regions has gained high attention within recent years. Analogous to weather routing, the occurrence of ice in a seaway affects the selection of the optimal route with respect to the travel time or fuel consumption. The shorter, direct path between two points—which may lead through an ice-covered area—may require a reduction of speed and an increase in fuel consumption. A longer, indirect route, could be more efficient by avoiding the ice-covered region. Certain regions may have to be avoided completely, if the ice thickness exceeds the ice-capability of the ship. The objective of this study is to develop a computational method that combines coastline maps, route cost information (e.g., ice thickness), transport task, and ship properties to find the optimal route between port of departure, A, and port of destination, B. The development approach for this tool is to formulate the transport task in the form of a potential problem, solve this equation with a finite element method (FEM), and apply line integration and optimization to determine the best route. The functionality of the method is first evaluated with simple test problems and then applied to realistic transport scenarios.

A Computational Method for Modeling Interface Corner Crack under Steady-State Delamination

2012 ◽  
Vol 486 ◽  
pp. 457-463
Author(s):  
Badrinath Veluri ◽  
Henrik Myhre Jensen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Steady State ◽  
Crack Front ◽  
Strain Energy Release ◽  
Computational Method ◽  
The Finite Element Method ◽  
Corner Crack ◽  
Corner Cracks ◽  
Element Method

Corner cracks under steady-state delamination were investigated. The fracture mechanics parameters that include the strain energy release rate and the three-dimensional mode-mixity along the interface crack front are estimated. A numerical approach was then applied for coupling the far field solutions based on the Finite Element Method to the near field (crack tip) solutions based on the J-integral methodology. A quantitative approach was formulated based on the finite element method with iterative adjustment of the crack front nodal coordinates to estimate the critical delamination stresses as a function of the fracture criterion and corner angles.

A Localized Finite-Element Method for the Nonlinear Steady Waves Due to a Two-Dimensional Hydrofoil

1994 ◽  
Vol 38 (01) ◽  
pp. 42-51
Author(s):  
Kwang June Bai ◽  
Jae Hoon Han
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Surface ◽  
Computational Method ◽  
Experimental Measurements ◽  
Surface Boundary ◽  
Two Dimensional ◽  
True Solution ◽  
Nonlinear Free Surface ◽  
Element Method

An application is described of the localized finite-element method to a steady nonlinear free-surface flow past a submerged two-dimensional hydrofoil at an arbitrary angle of attack. The earlier investigations with the linear free-surface boundary condition have shown some disagreement between the computed results and the experimental measurements for the cases of shallow submergence. The aim of this paper is to investigate the effect of the nonlinear free-surface condition for the cases where the linear results show disagreement with the experimental measurements. The computational method of solution is the localized finite-element method based on the classical Hamilton's principle. In the present study, a notable step is introduced in the matching procedure between the fully nonlinear and the linear subdomains. The numerical results of wave resistance, lift force, and circulation strength are presented. The computed pressure distributions on the hydrofoil and wave profiles are shown and compared with the experimental measurements and also with the linear computational results. The present computed results show better agreement with the experimental results. In some cases, however, a difficulty in the convergence of the iterative solution procedure was experienced. This difficulty in the convergence may be due to the limit of the range of the existence of the true solution in potential-flow formulation.

Use of Jˆ-Integral in Dynamic Analysis of Cracked Linear Viscoelastic Solids by Finite-Element Method

1982 ◽  
Vol 49 (1) ◽  
pp. 75-80 ◽  
Author(s):  
K. Kishimoto ◽  
S. Aoki ◽  
M. Sakata
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Computational Method ◽  
Intensity Factors ◽  
Dynamic Stress Intensity Factors ◽  
Element Method

A computational method using the path (area)-independent Jˆ-integral is developed to analyze viscoelastic problems. Since the displacement field near the crack tip of a viscoelastic solid is dependent upon the complete past history of the dynamic stress-intensity factors, the Jˆ-integral is represented by a hereditary integral of the dynamic stress-intensity factors. We assume that the stress and strain rates vary in proportion to time during each increment of time and derive a formula to obtain the current value of the dynamic stress-intensity factor from the time increment of the Jˆ-value. Both pure and mixed mode problems of a suddenly loaded crack are analyzed by making use of the formula together with the conventional finite-element method. In order to demonstrate the capability and reliability of the present method, problems of a center crack and an oblique crack in viscoelastic rectangular plates are solved.

Moving least-squares finite element method

2007 ◽  
Vol 221 (9) ◽  
pp. 1019-1036 ◽  
Author(s):  
M Musivand-Arzanfudi ◽  
H Hosseini-Toudeshky
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Least Squares ◽  
Three Dimensional ◽  
Meshless Methods ◽  
Computational Method ◽  
Computational Time ◽  
Moving Least Squares ◽  
Shape Functions ◽  
Element Method

A new computational method here called moving least-squares finite element method (MLSFEM) is presented, in which the shape functions of the parametric elements are constructed using moving least-squares approximation. While preserving some excellent characteristics of the meshless methods such as elimination of the volumetric locking in near-incompressible materials and giving accurate strains and stresses near the boundaries of the problem, the computational time is decreased by constructing the meshless shape functions in the stage of creating parametric elements and then utilizing them for any new problem. Moreover, it is not necessary to have knowledge about the full details of the shape function generation method in future uses. The MLSFEM also eliminates another drawback of meshless methods associated with the lack of accordance between the integration cells and the problem boundaries. The method is described for two-dimensional problems, but it is extendable for three-dimensional problems too. The MLSFEM does not require the complex mesh generation. Excellent results can be obtained even using a simple mesh. A technique is also presented for isoparametric mapping which enables best possible mapping via a constrained optimization criterion. Several numerical examples are analysed to show the efficiency and convergence of the method.

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