scholarly journals Modifications of the Newton–Raphson method for finite element simulations in ferroelectroelasticity

2013 ◽  
Vol 50 (5) ◽  
pp. 773-780 ◽  
Author(s):  
S. Stark ◽  
S. Roth ◽  
P. Neumeister ◽  
H. Balke
Keyword(s):  
Finite Element ◽  
Finite Element Simulations ◽  
Newton Raphson ◽  
Raphson Method

Influence of Transverse Cracks on Ultimate Strength of a Steel Plate Under Compression

2011 ◽  
Author(s):  
Abbas Bayatfar ◽  
Jerome Matagne ◽  
Philippe Rigo
Keyword(s):  
Finite Element ◽  
Ultimate Strength ◽  
Steel Plate ◽  
Transverse Cracks ◽  
Longitudinal Compression ◽  
Initial Imperfections ◽  
Crack Location ◽  
Linear Finite Element ◽  
Newton Raphson ◽  
Raphson Method

This study has been carried out on ultimate compressive strength of a cracked steel plate component, considering the effects of initial imperfections (transverse and longitudinal residual stresses and initial deflection, as well). The main objective of this paper is to numerically investigate the influence of crack location and crack length on ultimate strength of a steel plate under monotonic longitudinal compression. This investigation is performed through non-linear finite element (FE) analysis using ANSYS commercial finite element code in which is employed Newton-Raphson method. The FE results indicate that the length of transverse crack and especially its location can significantly affect the magnitude of ultimate strength where the steel plate is subjected to longitudinal compressive action.

Improved Rotative Mid-Point Mensuration and Newton-Raphson Method in 2-D Flat Rolling Simulation

2011 ◽  
Vol 328-330 ◽  
pp. 1436-1439
Author(s):  
Shu Ni Song ◽  
Jing Yi Liu
Keyword(s):  
Finite Element ◽  
Simultaneous Equations ◽  
Rigid Plastic ◽  
Cpu Time ◽  
Numerical Tests ◽  
Element Simulation ◽  
Flat Rolling ◽  
Newton Raphson ◽  
Time Required ◽  
Raphson Method

Newton-Raphson (N-R) method has been employed to solve the system of simultaneous equations arising in Rigid-Plastic finite element simulation. The combination of the improved rotative mid-point mensuration and the N-R method, named the M-P method is designated to solve the equations of velocity increment in Rigid-Plastic FEM. The CPU times required for calculation by the M-P method and the N-R method are compared and it is found that the CPU time required for calculation of the N-R method is more than the M-P method. The calculated rolling forces by the M-P method and the N-R method are compared and it is found that the former correlates better with the measured value. Numerical tests and application show that the M-P method is feasible and steady.

Finite Element-Based Brownian Dynamics Simulation of Nanofiber Suspensions Using Monte Carlo Method1

2015 ◽  
Vol 3 (4) ◽  
Author(s):  
Dongdong Zhang ◽  
Douglas E. Smith
Keyword(s):  
Finite Element ◽  
Monte Carlo ◽  
Brownian Dynamics ◽  
Element Model ◽  
Dynamics Simulation ◽  
Brownian Dynamics Simulation ◽  
Fiber Motion ◽  
Newton Raphson ◽  
Raphson Method ◽  
Surrounding Fluid

This paper presents a computational approach for simulating the motion of nanofibers during fiber-filled composites processing. A finite element-based Brownian dynamics simulation (BDS) is proposed to solve for the motion of nanofibers suspended within a viscous fluid. We employ a Langevin approach to account for both hydrodynamic and Brownian effects. The finite element method (FEM) is used to compute the hydrodynamic force and torque exerted from the surrounding fluid. The Brownian force and torque are regarded as the random thermal disturbing effects which are modeled as a Gaussian process. Our approach seeks solutions using an iterative Newton–Raphson method for a fiber's linear and angular velocities such that the net forces and torques, including both hydrodynamic and Brownian effects, acting on the fiber are zero. In the Newton–Raphson method, the analytical Jacobian matrix is derived from our finite element model. Fiber motion is then computed with a Runge–Kutta method to update fiber position and orientation as a function of time. Instead of remeshing the fluid domain as a fiber migrates, the essential boundary condition is transformed on the boundary of the fluid domain, so the tedious process of updating the stiffness matrix of finite element model is avoided. Since the Brownian disturbance from the surrounding fluid molecules is a stochastic process, Monte Carlo simulation is used to evaluate a large quantity of motions of a single fiber associated with different random Brownian forces and torques. The final fiber motion is obtained by averaging numerous fiber motion paths. Examples of fiber motions with various Péclet numbers are presented in this paper. The proposed computational methodology may be used to gain insight on how to control fiber orientation in micro- and nanopolymer composite suspensions in order to obtain the best engineered products.

Dynamic Wrinkling of Viscoelastic Membranes

1993 ◽  
Vol 60 (3) ◽  
pp. 575-582 ◽  
Author(s):  
C. H. Jenkins ◽  
J. W. Leonard
Keyword(s):  
Finite Element ◽  
Constitutive Equation ◽  
Strain Energy ◽  
Temporal Integration ◽  
Nonlinear Finite Element ◽  
Analysis Method ◽  
Finite Difference Equation ◽  
Membrane Structures ◽  
Newton Raphson ◽  
Raphson Method

Problems associated with viscoelastic membrane structures have been documented, e.g., dynamic wrinkling and its effects on fatigue analysis and on snap loading. In the proposed analysis method, the constitutive equation is approximated by a finite difference equation and embedded within a nonlinear finite element spatial discretization. Implicit temporal integration and a modified Newton-Raphson method are used within a time increment. The stress-strain hereditary relation is formally derived from thermodynamic considerations. Use of modified strain-energy and dissipation functions facilitates the description of wrinkling during the analysis. Applications are demonstrated on an inflated cylindrical cantilever and on a submerged cylindrical membrane excited by waves.

Finite Element-Based Brownian Dynamics Simulation of Nano-Fiber Suspensions in Nano-Composites Processing Using Monte-Carlo Method

2012 ◽  
Author(s):  
Dongdong Zhang ◽  
Douglas E. Smith
Keyword(s):  
Finite Element ◽  
Brownian Dynamics ◽  
Element Model ◽  
Dynamics Simulation ◽  
Nano Composites ◽  
Brownian Dynamics Simulation ◽  
Fiber Motion ◽  
Newton Raphson ◽  
Composites Processing ◽  
Raphson Method

This paper presents a computational approach for simulating the motion of nano-fibers during polymer nano-composites processing. A finite element-based Brownian dynamics simulation is proposed to solve the motion of nano-fibers suspended within a viscous fluid. In this paper, a Langevin approach is used to account for both hydrodynamic and Brownian effects. We develop a stand-alone Finite Element Method (FEM) for modeling the hydrodynamic effect exerted from the surrounding fluid. The Brownian effects are regarded as the random thermal disturbing forces/torques, which are modeled as a Gaussian process. Our approach seeks solutions using an iterative Newton-Raphson method for the fiber’s linear and angular velocities such that the net forces and torques, i.e. the combination of hydrodynamic and Brownian effects, acting on the fiber are zero. In the Newton-Raphson method, the analytical Jacobian matrix is derived from our finite element model. Fiber motion is then computed with a Runge-Kutta method to update the fiber positions and orientations as a function of time. Instead of re-meshing the fluid domain as fiber moves, we applied the transformed essential boundary conditions on the boundary of fluid domain, so the tedious process of updating stiffness matrix of finite element model is avoided. Since Brownian disturbance from the fluid molecules is a stochastic process, Monte-Carlo simulation is used to evaluate the motion of a great many fibers associated with different random Brownian forces and torques. The final fiber motion is obtained by averaging a numerous fiber motion paths. Examples of fiber motions with various Péclet numbers are presented in this paper. The proposed computational methodology will be used to gain insight on how to control fiber orientations in micro- and nano-polymer composite suspensions in order to obtain the best engineered products.

scholarly journals A Vector Play Model for Finite-Element Eddy-Current Analysis Using the Newton-Raphson Method

2013 ◽  
Vol 49 (5) ◽  
pp. 1689-1692 ◽  
Author(s):  
Ryuhei Mitsuoka ◽  
Takeshi Mifune ◽  
Tetsuji Matsuo ◽  
Chikara Kaido
Keyword(s):  
Finite Element ◽  
Eddy Current ◽  
Current Analysis ◽  
Newton Raphson ◽  
Raphson Method
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