Nonlinear Dynamics of Rigid and Flexible Multibody Systems

1999 ◽  
Author(s):  
Evtim V. Zakhariev
Keyword(s):  
Finite Elements ◽  
Multibody Systems ◽  
Virtual Work ◽  
Space Station ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Numerical Approach ◽  
Dynamic Equations ◽  
Dynamics Modeling ◽  
Lagrange Equations

Abstract In the present paper a unified numerical approach for dynamics modeling of multibody systems with rigid and flexible bodies is suggested. The dynamic equations are second order ordinary differential equations (without constraints) with respect to a minimal set of generalized coordinates that describe the parameters of gross relative motion of the adjacent bodies and their small elastic deformations. The numerical procedure consists of the following stages: structural decomposition of elastic links into fictitious rigid points and/or bodies connected by joints in which small force dependent relative displacements are achieved; kinematic analysis; deriving explicit form dynamic equations. The algorithm is developed in case of elastic slender beams and finite elements achieving spatial motion with three translations and three rotations of nodes. The beam elements are basic design units in many mechanical devices as space station antennae and manipulators, cranes and etc. doing three dimensional motion which large elastic deflections could not be neglected or linearised. The stiffness coefficients and inertia mass parameters of the fictitious joints and links are calculated using the numerical procedures of the finite element theory. The method is called finite elements in relative coordinates. Its equivalence with the procedures of recently developed finite segment approaches is shown, while in the treatment different results are obtained. The approach is used for solution of some nonlinear static problems and for deriving the explicit configuration space dynamic equations of spatial flexible system using the principle of virtual work and Euler-Lagrange equations.

Thermal jet drilling of granite rock: a numerical 3D finite-element study

2021 ◽  
Vol 379 (2196) ◽  
pp. 20200128
Author(s):  
Timo Saksala ◽  
Reijo Kouhia ◽  
Ahmad Mardoukhi ◽  
Mikko Hokka
Keyword(s):  
Finite Elements ◽  
Numerical Study ◽  
Thermal Flux ◽  
Three Dimensional ◽  
Numerical Approach ◽  
Mass Scaling ◽  
Granite Rock ◽  
Fracture Dynamics ◽  
Rock Heterogeneity ◽  
Thermal Drilling

This paper presents a numerical study on thermal jet drilling of granite rock that is based on a thermal spallation phenomenon. For this end, a numerical method based on finite elements and a damage–viscoplasticity model are developed for solving the underlying coupled thermo-mechanical problem. An explicit time-stepping scheme is applied in solving the global problem, which in the present case is amenable to extreme mass scaling. Rock heterogeneity is accounted for as random clusters of finite elements representing rock constituent minerals. The numerical approach is validated based on experiments on thermal shock weakening effect of granite in a dynamic Brazilian disc test. The validated model is applied in three-dimensional simulations of thermal jet drilling with a short duration (0.2 s) and high intensity (approx. 3 MW m −2 ) thermal flux. The present numerical approach predicts the spalling as highly (tensile) damaged rock. Finally, it was shown that thermal drilling exploiting heating-forced cooling cycles is a viable method when drilling in hot rock mass. This article is part of the theme issue ‘Fracture dynamics of solid materials: from particles to the globe’.

Impact and Bifurcation of Flexible Multibody Systems

2003 ◽  
Author(s):  
Evtim V. Zahariev
Keyword(s):  
Finite Elements ◽  
Eigenvalue Problem ◽  
Multibody Systems ◽  
Dynamic Equations ◽  
Loss Of Stability ◽  
Motion Simulation ◽  
Novel Approach ◽  
Spatial Systems ◽  
Relative Coordinates ◽  
Initial Forms

In the paper, the process of loss of stability of multibody systems and structures is analyzed. A novel approach is presented and applied as for the statically loaded spatial systems so for analysis of dynamic response of systems imposed on impact. The analysis is based on solution of the dynamic equations and eigenvalue problem of systems, and of resultant motion simulation. The flexible systems are discretized using the method of finite elements. The dynamic equations are derived with respect to the relative coordinates of the finite elements. Large flexible deflections due to loss of stability are simulated. The initial forms of the possible deformations are defined by the eigenvectors computed solving the eigenvalue problem for the system stiffness matrix. The critical forces and system deflections obtained due to percussive forces and impact are then analyzed. Examples of bifurcation of beam and beam structure imposed on compulsive motion, percussive forces and impact are presented.

A Corotational Approach for 3D Absolute Nodal Coordinate Elements

2009 ◽  
Author(s):  
Johannes Gerstmayr
Keyword(s):  
Finite Elements ◽  
Virtual Work ◽  
Mass Matrix ◽  
Three Dimensional ◽  
Simple Formulation ◽  
Absolute Nodal Coordinate ◽  
Practical Applications ◽  
Elastic Forces ◽  
Linearized Model ◽  
Small Deformations

The present paper deals with the modeling of three dimensional (3D), nonlinear beam finite elements which do not employ rotational parameters. The beam elements are based on the so-called absolute nodal coordinate formulation (ANCF), which has been introduced in the late 1990’s. Early implementations of 3D ANCF beam finite elements incorporated problems regarding Poisson, thickness and shear locking. In the present paper, two alternative models for the work of elastic forces are presented. The first approach, which is intended to provide reference solutions, is close to the original approach. However, the effect of Poisson and thickness locking is eliminated by proper integration of the contributing terms in the virtual work of elastic forces. In the second approach, a corotationally linearized model is developed, which is based on a simple formulation for the elastic forces. The latter model only takes into account small deformations with respect to a corotating reference frame, but it is different from the conventional floating frame of reference formulation, because it has a constant mass matrix. The second approach is intended to be advantageous in practical applications where only small deformations with respect to large rigid body motions need to be taken into account, such as in robotics or machine dynamics. Numerical results are presented, which show that the new approaches agree with the solution of static and dynamic problems using classical finite elements or analytical methods.

Numerical Computation of Differential-Algebraic Equations for Non-Linear Dynamics of Multibody Systems Involving Contact Forces

1999 ◽  
Vol 123 (2) ◽  
pp. 272-281 ◽  
Author(s):  
B. Fox ◽  
L. S. Jennings ◽  
A. Y. Zomaya
Keyword(s):  
Multibody Systems ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Variational Problems ◽  
Differential Algebraic Equations ◽  
Contact Forces ◽  
Algebraic Equations ◽  
Differential Algebraic Equation ◽  
Lagrange Equations ◽  
Constraint Equations

The well known Euler-Lagrange equations of motion for constrained variational problems are derived using the principle of virtual work. These equations are used in the modelling of multibody systems and result in differential-algebraic equations of high index. Here they concern an N-link pendulum, a heavy aircraft towing truck and a heavy off-highway track vehicle. The differential-algebraic equation is cast as an ordinary differential equation through differentiation of the constraint equations. The resulting system is computed using the integration routine LSODAR, the Euler and fourth order Runge-Kutta methods. The difficulty to integrate this system is revealed to be the result of many highly oscillatory forces of large magnitude acting on many bodies simultaneously. Constraint compliance is analyzed for the three different integration methods and the drift of the constraint equations for the three different systems is shown to be influenced by nonlinear contact forces.

Symbolic Closed-Form Modeling and Linearization of Multibody Systems Subject to Control

1991 ◽  
Vol 113 (2) ◽  
pp. 124-132 ◽  
Author(s):  
Junghsen Lieh ◽  
Imtiaz-ul Haque
Keyword(s):  
Closed Form ◽  
Multibody Systems ◽  
Space Form ◽  
Virtual Work ◽  
Dynamic Equations ◽  
Principle Of Virtual Work ◽  
Constraint Forces ◽  
Active Suspensions ◽  
Linear Dynamic ◽  
Curved Track

Symbolic closed-form equation formulation and linearization for constrained multibody systems subject to control are presented. The formulation is based on the principle of virtual work. The algorithm is recursive, automatically eliminates the constraint forces and redundant coordinates, and generates the nonlinear or linear dynamic equations in closed-form. It is derived with respect to principal body coordinates and a moving reference frame that allows one to generate the dynamic equations for multibody systems moving along curved track or road. The output equations may be either in syntactically correct FORTRAN form or in the form as derived by hand. A procedure that simplifies the trigonometric expressions, linearizes the geometric nonlinearities, and converts the linearized equations in state-space form is included. Several examples have been used to validate the procedure. Included is a simulation using a seven-DOF automobile ride model with active suspensions.

scholarly journals Numerical modeling of the contact between three-dimensional regions with the use of FEM

2018 ◽  
Vol 157 ◽  
pp. 08009
Author(s):  
Tomasz Skrzypczak ◽  
Ewa Węgrzyn-Skrzypczak ◽  
Leszek Sowa
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Modeling ◽  
Finite Elements ◽  
Three Dimensional ◽  
Numerical Approach ◽  
Mechanical Interaction ◽  
The Finite Element Method ◽  
Three Dimensional Objects ◽  
Original Program

The numerical approach based on the finite element method (FEM) for modeling of mechanical interaction between three-dimensional objects is presented in the paper. The model of contact is based on the assumption that the nodes of the region which is the source of contact cannot overlap with the nodes of the region being the target. The procedure of the detection of collision between surfaces of the source and the target is discussed in details. The behaviour of surfaces being in contact depends on their rigidity and is numerically modeled in the case of perfectly rigid source and deformable target. Each modeled object has an independent mesh of finite elements. These meshes can be freely moved relative to each other. Example of calculation using original program written in C++ is presented and discussed.

Modeling and Assessment of the Produced Water Discharges from Offshore Petroleum Platforms

2007 ◽  
Vol 42 (4) ◽  
pp. 303-310 ◽  
Author(s):  
Zhi Chen ◽  
Lin Zhao ◽  
Kenneth Lee ◽  
Charles Hannath
Keyword(s):  
Random Walk ◽  
Produced Water ◽  
Model Development ◽  
Three Dimensional ◽  
Monitoring Program ◽  
Ecological Monitoring ◽  
Numerical Approach ◽  
Ocean Model ◽  
Scale Model ◽  
Water Stream

Abstract There has been a growing interest in assessing the risks to the marine environment from produced water discharges. This study describes the development of a numerical approach, POM-RW, based on an integration of the Princeton Ocean Model (POM) and a Random Walk (RW) simulation of pollutant transport. Specifically, the POM is employed to simulate local ocean currents. It provides three-dimensional hydrodynamic input to a Random Walk model focused on the dispersion of toxic components within the produced water stream on a regional spatial scale. Model development and field validation of the predicted current field and pollutant concentrations were conducted in conjunction with a water quality and ecological monitoring program for an offshore facility located on the Grand Banks of Canada. Results indicate that the POM-RW approach is useful to address environmental risks associated with the produced water discharges.

Simulation of small-angle scattering curves by numerical Fourier transformation

2007 ◽  
Vol 40 (1) ◽  
pp. 16-25 ◽  
Author(s):  
Klaus Schmidt-Rohr
Keyword(s):  
Form Factor ◽  
Small Angle ◽  
Fourier Transformation ◽  
Three Dimensional ◽  
Power Laws ◽  
Numerical Approach ◽  
Peak Position ◽  
Two Dimensions ◽  
Correlation Peak ◽  
Scattering Intensity

A simple numerical approach for calculating theq-dependence of the scattering intensity in small-angle X-ray or neutron scattering (SAXS/SANS) is discussed. For a user-defined scattering density on a lattice, the scattering intensityI(q) (qis the modulus of the scattering vector) is calculated by three-dimensional (or two-dimensional) numerical Fourier transformation and spherical summation inqspace, with a simple smoothing algorithm. An exact and simple correction for continuous rather than discrete (lattice-point) scattering density is described. Applications to relatively densely packed particles in solids (e.g.nanocomposites) are shown, where correlation effects make single-particle (pure form-factor) calculations invalid. The algorithm can be applied to particles of any shape that can be defined on the chosen cubic lattice and with any size distribution, while those features pose difficulties to a traditional treatment in terms of form and structure factors. For particles of identical but potentially complex shapes, numerical calculation of the form factor is described. Long parallel rods and platelets of various cross-section shapes are particularly convenient to treat, since the calculation is reduced to two dimensions. The method is used to demonstrate that the scattering intensity from `randomly' parallel-packed long cylinders is not described by simple 1/qand 1/q4power laws, but at cylinder volume fractions of more than ∼25% includes a correlation peak. The simulations highlight that the traditional evaluation of the peak position overestimates the cylinder thickness by a factor of ∼1.5. It is also shown that a mix of various relatively densely packed long boards can produceI(q) ≃ 1/q, usually observed for rod-shaped particles, without a correlation peak.

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