About the use of standard integration schemes for X-FEM in solid mechanics plasticity

2015 ◽  
Vol 283 ◽  
pp. 551-572 ◽  
Author(s):  
A. Martin ◽  
J.-B. Esnault ◽  
P. Massin
Keyword(s):  
Solid Mechanics ◽  
Integration Schemes ◽  
Standard Integration

Advanced Cyclic Plasticity Models in Simulating Ratcheting Responses of Straight and Elbow Piping Components, and Notched Plates

2005 ◽  
Author(s):  
Syed M. Rahman ◽  
Tasnim Hassan
Keyword(s):  
Damage Accumulation ◽  
Solid Mechanics ◽  
Fatigue Cracks ◽  
Constitutive Models ◽  
Local Stress ◽  
Weather Conditions ◽  
Operating Conditions ◽  
Cyclic Plasticity ◽  
Integration Schemes ◽  
Current State

Ratcheting is defined as the accumulation of strain or deformation in structures under cyclic loading. Damage accumulation due to ratcheting can cause failure of structures through fatigue cracks or plastic collapse. Ratcheting damage accumulation in structures may occur under repeated reversals of loading induced by earthquakes, extreme weather conditions, and mechanical and thermal operating conditions. A major challenge in structural and solid mechanics is the prediction of ratcheting responses of structures under any or combination of these loading conditions. Accurate prediction of ratcheting-fatigue and ratcheting-collapse is imperative in order to incorporate the ratcheting related failures into the ASME design Code in a rational manner. This would require predictions of both local (stress-strain) and global (load-deflection) responses simultaneously. In progressing towards this direction, a set of experimental ratcheting responses for straight and elbow piping components and notched plates is developed. Advanced cyclic plasticity models, such as, modified Chaboche, Ohno-Wang, and AbdelKarim-Ohno models, are implemented in ANSYS for simulation of these experimental responses. Various integration schemes for implementing the constitutive models into the structural analysis code ANSYS are studied. Results from the experimental and analytical studies are presented and discussed in order to demonstrate the current state of simulation modeling of structural ratcheting.

New Polyhedral Elements Based on Virtual Node Method for Solid Mechanics and Heat Transfer Applications

2014 ◽  
Vol 493 ◽  
pp. 367-371 ◽  
Author(s):  
Logah Perumal ◽  
M.I. Fadhel
Keyword(s):  
Heat Transfer ◽  
Solid Mechanics ◽  
Shape Functions ◽  
Virtual Node ◽  
Established Method ◽  
Exact Integration ◽  
3 Dimensional ◽  
Integration Schemes ◽  
Engineering Problems ◽  
Complex Engineering

Finite element method (FEM) is a well-established method and commonly utilized to solve complex engineering problems which cannot be solved analytically. Various element types have been formulated over the years to facilitate engineering analyses using FEM. In this paper, new polyhedral elements are developed by utilizing virtual node method. This paper covers the formulation of shape functions and integration schemes for the new polyhedral elements. These new polyhedral elements have advantages due to the nature of their shape functions which consist of monomials uavbwc. Integration of functions within the element can be accomplished by utilizing an exact integration technique. These polyhedral elements can be utilized to solve real 3 dimensional problems which arise in solid mechanics and heat transfer phenomena.

Incompressibility in Dynamic Relaxation

1987 ◽  
Vol 54 (3) ◽  
pp. 539-544 ◽  
Author(s):  
S. A. Silling
Keyword(s):  
Solid Mechanics ◽  
Linear Equations ◽  
Time Integration ◽  
Natural State ◽  
System Of Linear Equations ◽  
Dynamic Relaxation ◽  
Explicit Time Integration ◽  
Integration Schemes ◽  
Time Integration Schemes ◽  
Incompressibility Constraint

A method is described for enforcing the incompressibility constraint in large-deformation solid mechanics computations using dynamic relaxation. The method is well-suited to explicit time-integration schemes because it does not require the solution of a system of linear equations. It is based on an analogy with thermoelasticity involving manipulation of the natural state of a solid.

scholarly journals A Convenient Approximation of the Projectile Motion with Quadratic Air Resistance

2021 ◽  
Author(s):  
Marc Landon
Keyword(s):  
Analytic Solution ◽  
The Body ◽  
Integration Scheme ◽  
Reduction Principle ◽  
Initial State ◽  
Resistive Force ◽  
Projectile Motion ◽  
Integration Schemes ◽  
Air Resistance ◽  
Standard Integration

Abstract A convenient approximated analytic solution is proposed for the problem of the motion of a body under a resistive force, acting in the magnitude of the squared velocity of the body. This solution is an explicit function of time, that keeps a good behavior both near the initial state and far from the initial state. To obtain a general analytic solution, we firstly used a reduction principle to be able to manipulate scalar objects, and we analyzed limit behaviors, both near the initial state and far from the initial state. Secondly, we proposed an approximated analytic solution with heuristics based on the built knowledge. Finally, a robust and stable integration scheme is proposed, based on the obtained analytic solution. We compared the scheme with other standard integration schemes.

Order and Chaos in a Discrete Duffing Oscillator: Implications on Numerical Integration

1989 ◽  
Vol 56 (1) ◽  
pp. 162-167 ◽  
Author(s):  
P. G. Reinhall ◽  
T. K. Caughey ◽  
D. W. Storti
Keyword(s):  
Numerical Integration ◽  
Duffing Oscillator ◽  
Continuous System ◽  
Elliptic Functions ◽  
Alternative Scheme ◽  
Integration Schemes ◽  
Time Problem ◽  
Analytic Expressions ◽  
Homoclinic Tangles ◽  
Standard Integration

In this paper, we study the dynamics of some two-dimensional mappings which arise when standard numerical integration schemes are applied to an unforced oscillator with a cubic stiffness nonlinearity, i.e., the Duffing equation. While the continuous time problem is integrable and is solved analytically in terms of Jacobi elliptic functions, the discrete versions of this simple system arising from standard integration schemes exhibit very complicated dynamics due to the presence of homoclinic tangles. We present an alternative scheme for discretizing the nonlinear term which preserves the integrable dynamics of the continuous system and derive analytic expressions for the orbits and invariant curves of the resulting mapping.

A GFEM With Local Gradient Smoothed Approximation for 2D Solid Mechanics Problems

2020 ◽  
Author(s):  
Jinsong Tang ◽  
Linfang Qian ◽  
Guangsong Chen
Keyword(s):  
Finite Element ◽  
Basis Function ◽  
Taylor Expansion ◽  
Solid Mechanics ◽  
Shape Function ◽  
Displacement Function ◽  
Field Function ◽  
Integration Schemes ◽  
Local Gradient ◽  
Element Shape

Abstract In this paper, a generalized finite element method (GFEM) with local gradient smoothed approximation (LGS-GFEM) using triangular meshes is proposed. The displacement field function of LGS-GFEM consists of the finite element shape function and the node displacement function. In order to obtain the nodal displacement function, the second order Taylor expansion is considered. The derivative term in Taylor expansion is obtained by using gradient smoothed technique in a smoothed domain. The displacement in smoothed operation is interpolated by polynomial basis function and radial basis function. Two kinds of integration schemes are considered, i.e. LGS-GFEM-I and LGS-GFEM-II respectively. The smoothed composite shape function of LGS-GFEM retains the ideal Kronecker property of the finite element shape function. Besides, the proposed LGS-GFEM has some other important properties such as no extra DOFs, linear independent, etc. The superiority of LGS-GFEM including high accuracy, rapid error convergence and temporal stability, is demonstrated by two representative numerical examples of static and free vibration, and compared with the classical finite element of triangular (FEM-T3) and quadrilateral (FEM-Q4) elements.

Alternative stress-integration schemes for large-deformation problems of solid mechanics

2009 ◽  
Vol 45 (12) ◽  
pp. 934-943 ◽  
Author(s):  
Majidreza Nazem ◽  
John P. Carter ◽  
Daichao Sheng ◽  
Scott W. Sloan
Keyword(s):  
Large Deformation ◽  
Solid Mechanics ◽  
Integration Schemes ◽  
Stress Integration ◽  
Large Deformation Problems

Applied Solid Mechanics

2001 ◽  
Author(s):  
Peter Howell ◽  
Gregory Kozyreff ◽  
John Ockendon
Keyword(s):  
Solid Mechanics

Air Bridge Technology: A Comparison of Novel Interconnect Materials and Integration Schemes for Beyond 45 nm

2003 ◽  
Vol 766 ◽  
Author(s):  
Kenneth Foster ◽  
Joost Waeterloos ◽  
Don Frye ◽  
Steve Froelicher ◽  
Mike Mills
Keyword(s):  
Dielectric Constants ◽  
Advanced Technology ◽  
Effective Dielectric Constant ◽  
Device Performance ◽  
Interlayer Dielectric ◽  
Integration Schemes ◽  
Stepwise Reduction ◽  
Bridge Technology ◽  
Integrated Device ◽  
Compare And Contrast

AbstractThe electronics industry, in a continual drive for improved integrated device performance, is seeking increasingly lower dielectric constants (k) of the insulators that are used as interlayer dielectric (ILD) for advanced logic interconnects. As the industry continually seeks a stepwise reduction of the “effective” dielectric constant (keff), simple extendibility, leads to the consideration of the highest performance possible, namely air bridge technology. In this paper we will discuss requirements, integration schemes and properties for a novel class of materials that has been developed as part of an advanced technology probe into air bridge architecture. We will compare and contrast these potential technology offerings with other existing dense and porous ILD integration options, and show that the choice is neither trivial nor obvious.

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