Modeling of Deformable Tire and Soil Interaction Using Multiplicative Finite Plasticity for Multibody Off-Road Mobility Simulation

2016 ◽  
Author(s):  
Hiroki Yamashita ◽  
Paramsothy Jayakumar ◽  
Hiroyuki Sugiyama
Keyword(s):  
Numerical Procedure ◽  
Interaction Model ◽  
Position Vector ◽  
Computer Algorithms ◽  
Time Step ◽  
Soil Model ◽  
Highly Nonlinear ◽  
Assumed Strain ◽  
Brick Element ◽  
Interaction Simulation

The objective of this study is to develop a physics-based tire/soil interaction model that can be fully integrated into general multibody dynamics computer algorithms. To this end, a continuum soil model using multiplicative plasticity theory with Drucker-Prager failure criterion is integrated with the high-fidelity flexible tire model developed using the shear deformable laminated composite shell elements for deformable tire/terrain interaction simulation. The element locking of the standard 8-node brick element caused by the tri-linear polynomial can be alleviated by introducing an additional node defining the second derivative of the global position vector at the center of the element, allowing for describing the linear strain distribution over the element volume without introducing enhanced assumed strain (EAS). The benchmark test result indicates that the identical rate of convergence to that of the locking-free 8-node brick element with 9-parameter EAS is obtained using the brick element presented in this study. Since the constitutive equation for soil models is highly nonlinear in nature, involving iterative return mapping algorithm to find the plastic strain every time step, elimination of EAS using the 9-node brick element leads to straightforward implementation for soil model and computationally efficient procedure for tire/soil interaction simulation. Numerical example of deformable tire and terrain interaction simulation is presented to demonstrate the numerical procedure developed in this study.

scholarly journals Physics-Based Deformable Tire–Soil Interaction Model for Off-Road Mobility Simulation and Experimental Validation

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Hiroki Yamashita ◽  
Paramsothy Jayakumar ◽  
Mustafa Alsaleh ◽  
Hiroyuki Sugiyama
Keyword(s):  
Simulation Model ◽  
Multibody Dynamics ◽  
Test Data ◽  
Interaction Model ◽  
Computational Time ◽  
Test Results ◽  
Soil Model ◽  
Interaction Simulation ◽  
Patch Technique ◽  
Soil Patch

A physics-based deformable tire–soil interaction simulation capability that can be fully integrated into the monolithic multibody dynamics computer algorithm is developed by extending a deformable tire model based on the flexible multibody dynamics approach to off-road mobility simulations with a moving soil patch technique and it is validated against test data. A locking-free nine-node brick element is developed for modeling large plastic soil deformation using the multiplicative finite strain plasticity theory along with the capped Drucker–Prager failure criterion. To identify soil parameters including cohesion and friction angle, the triaxial compression test is carried out, and the soil model developed is validated against the test data. In addition to the component level validation for the tire and soil models, the tire–soil interaction simulation capability developed in this study is validated against the soil bin mobility test results. The tire forces and rolling resistance coefficients predicted by the simulation model agree well with the test results. It is shown that effect of the wheel loads and tire inflation pressures is well captured in the simulation model. Furthermore, it is demonstrated that the moving soil patch technique, with which soil behavior only in the vicinity of the rolling tire is solved to reduce the soil model dimensionality, leads to a significant reduction in computational time, thereby enabling use of the high-fidelity physics-based tire–soil interaction model in the large-scale off-road mobility simulation.

NUMERICAL SOLUTIONS OF 2D AND 3D SLAMMING PROBLEMS

2021 ◽  
Vol 153 (A2) ◽  
Author(s):  
Q Yang ◽  
W Qiu
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Type Equation ◽  
The Body ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Highly Nonlinear ◽  
2D And 3D

Slamming forces on 2D and 3D bodies have been computed based on a CIP method. The highly nonlinear water entry problem governed by the Navier-Stokes equations was solved by a CIP based finite difference method on a fixed Cartesian grid. In the computation, a compact upwind scheme was employed for the advection calculations and a pressure-based algorithm was applied to treat the multiple phases. The free surface and the body boundaries were captured using density functions. For the pressure calculation, a Poisson-type equation was solved at each time step by the conjugate gradient iterative method. Validation studies were carried out for 2D wedges with various deadrise angles ranging from 0 to 60 degrees at constant vertical velocity. In the cases of wedges with small deadrise angles, the compressibility of air between the bottom of the wedge and the free surface was modelled. Studies were also extended to 3D bodies, such as a sphere, a cylinder and a catamaran, entering calm water. Computed pressures, free surface elevations and hydrodynamic forces were compared with experimental data and the numerical solutions by other methods.

Three-Dimensional Solid Brick Element Using Slopes in the Absolute Nodal Coordinate Formulation

2013 ◽  
Vol 9 (2) ◽  
Author(s):  
Alexander Olshevskiy ◽  
Oleg Dmitrochenko ◽  
Chang-Wan Kim
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Absolute Nodal Coordinate Formulation ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Test Problems ◽  
Absolute Nodal Coordinate ◽  
Highly Nonlinear ◽  
Brick Element ◽  
The Absolute

The present paper contributes to the field of flexible multibody systems dynamics. Two new solid finite elements employing the absolute nodal coordinate formulation are presented. In this formulation, the equations of motion contain a constant mass matrix and a vector of generalized gravity forces, but the vector of elastic forces is highly nonlinear. The proposed solid eight node brick element with 96 degrees of freedom uses translations of nodes and finite slopes as sets of nodal coordinates. The displacement field is interpolated using incomplete cubic polynomials providing the absence of shear locking effect. The use of finite slopes describes the deformed shape of the finite element more exactly and, therefore, minimizes the number of finite elements required for accurate simulations. Accuracy and convergence of the finite element is demonstrated in nonlinear test problems of statics and dynamics.

Numerical Investigation on the Vibration of Steam Turbine Inlet Valves and the Feedback to the Dynamic Flow Field

2015 ◽  
Author(s):  
Clemens Bernhard Domnick ◽  
Friedrich-Karl Benra ◽  
Dieter Brillert ◽  
Hans Josef Dohmen ◽  
Christian Musch
Keyword(s):  
Steam Turbine ◽  
Structural Dynamics ◽  
Fluid Dynamic ◽  
Dynamic Flow ◽  
Piston Rings ◽  
Time Step ◽  
Structural Dynamic ◽  
Turbine Inlet ◽  
Valve Stem ◽  
Highly Nonlinear

The power output of steam turbines is controlled by steam turbine inlet valves. These valves have a large flow capacity and dissipate in throttled operation a huge amount of energy. Due to that, high dynamic forces occur in the valve which can cause undesired valve vibrations. In this paper, the structural dynamics of a valve are analysed. The dynamic steam forces obtained by previous computational fluid dynamic (CFD) calculations at different operating points are impressed on the structural dynamic finite element model (FEM) of the valve. Due to frictional forces at the piston rings and contact effects at the bushings of the valve plug and the valve stem the structural dynamic FEM is highly nonlinear and has to be solved in the time domain. Prior to the actual investigation grid and time step studies are carried out. Also the effect of the temperature distribution within the valve stem is discussed and the influence of the valve actuator on the vibrations is analysed. In the first step, the vibrations generated by the fluid forces are investigated. The effects of the piston rings on the structural dynamics are discussed. It is found, that the piston rings are able to reduce the vibration significantly by frictional damping. In the second step, the effect of the moving valve plug on the dynamic flow in the valve is analysed. The time dependent displacement of the valve is transferred to CFD calculations using deformable meshes. With this one way coupling method the response of the flow to the vibrations is analysed.

Numerical Solution of 3-D Water Entry Problems With a Constrained Interpolation Profile Method

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Qingyong Yang ◽  
Wei Qiu
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Type Equation ◽  
Water Entry ◽  
Navier Stokes ◽  
Time Step ◽  
Constrained Interpolation ◽  
Navier Stokes Equations ◽  
Highly Nonlinear ◽  
Calm Water

This paper presents the numerical solutions of slamming problems for 3D bodies entering calm water with vertical and oblique velocities. The highly nonlinear water entry problems are governed by the Navier-Stokes equations and were solved by a constrained interpolation profile (CIP)-based finite difference method on a fixed Cartesian grid. In the computation, the 3D CIP method was employed for the advection calculations and a pressure-based algorithm was applied for the nonadvection calculations. The solid body and the free surface interfaces were captured by density functions. For the pressure computation, a Poisson-type equation was solved at each time step by using the conjugate gradient iterative method. Validation studies were carried out for a 3D wedge, a cusped body vertically entering calm water, and the oblique entry of a sphere into calm water. The predicted hydrodynamic forces on the wedge, the cusped body, and the sphere were compared with experimental data.

A Model For Diffusion and Competition in Cancer Growth and Metastasis

1997 ◽  
Vol 489 ◽  
Author(s):  
G. P. Pescarmona ◽  
M. Scalerandi ◽  
P. P. Delsanto ◽  
C. A. Condat
Keyword(s):  
Numerical Procedure ◽  
Local Environment ◽  
Coupled System ◽  
Cancer Growth ◽  
C Cells ◽  
Simulation Approach ◽  
Multiple Tumor ◽  
Suitable Parameter ◽  
Interaction Simulation ◽  
Stochastic Mechanism

AbstractA master equation formalism is used to model the growth and metastasis of a tumor as a function of the diffusion and absorption of a nutrient. Healthy and cancerous (C-) cells compete to bind the nutrient, which is allowed to diffuse starting from a prescribed region. Two thresholds are defined for the quantity of nutrient bound by the C-cells. If this quantity falls below the lower threshold, the cell dies, while if it increases above the upper threshold, the cell divides according to a predefined stochastic mechanism. C-cells migrate when they record a low concentration of free nutrient in the local environment. The model is formulated in terms of a coupled system of equations for the cell populations and the free and bound nutrient. This system can be solved by using the Local Interaction Simulation Approach (LISA), a numerical procedure that permits an efficient and detailed solution and is easily adaptable to parallel processing. With suitable parameter variation, the model can describe multiple tumor configurations, ranging from the classical spheroid with a necrotic core favored by mathematicians to very anisotropic shapes with inhomogeneous concentrations of the various populations. This is important because the nature of the anisotropy may be crucial in determining whether and how the cancer metastasizes. The effects of stochasticity and the presence of additional nutrients or inhibitors can be easily incorporated.

Nonlinear Numerical Prediction of Gas Foil Bearing Stability and Unbalanced Response

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Sébastien Le Lez ◽  
Mihaï Arghir ◽  
Jean Frêne
Keyword(s):  
Dry Friction ◽  
Stability Limit ◽  
Time Step ◽  
Structural Dynamic ◽  
Friction Forces ◽  
Foil Bearings ◽  
Mass Unbalance ◽  
Foil Bearing ◽  
Highly Nonlinear ◽  
The Stability

One of the main interests of gas foil bearings lies in their superior rotordynamic characteristics compared with conventional bearings. A numerical investigation on the stability limit and on the unbalanced response of foil bearings is presented in this paper. The main difficulty in modeling the dynamic behavior of such bearings comes from the dry friction that occurs within the foil structure. Indeed, dry friction is highly nonlinear and is strongly influenced by the dynamic amplitude of the pressure field. To deal with these nonlinearities, a structural dynamic model has been developed in a previous work. This model considers the entire corrugated foil and the interactions between the bumps by describing the foil bearing structure as a multiple degrees of freedom system. It allows the determination of the dynamic friction forces at the top and at the bottom of the bumps by simple integration of ordinary differential equations. The dynamic displacements of the entire corrugated sheet are then easily obtained at each time step. The coupling between this structural model and a gas bearing prediction code is presented in this paper and allows performing full nonlinear analyses of a complete foil bearing. The bearing stability is the first investigated problem. The results show that the structural deflection enhances the stability of compliant surface bearings compared with rigid ones. Moreover, when friction is introduced, a new level of stability is reached, revealing the importance of this dissipation mechanism. The second investigated problem is the unbalanced response of foil bearings. The shaft trajectories depict a nonlinear jump in the response of both rigid and foil bearings when the value of the unbalance increases. Again, it is evidenced that the foil bearing can support higher mass unbalance before this undesirable step occurs.

Large Displacement Analysis of a Marine Riser

1985 ◽  
Vol 107 (1) ◽  
pp. 54-59 ◽  
Author(s):  
T. Huang ◽  
S. Chucheepsakul
Keyword(s):  
Strain Energy ◽  
Equilibrium Configuration ◽  
Numerical Procedure ◽  
Stationary Condition ◽  
Arc Length ◽  
Algebraic Equations ◽  
The Finite Element Method ◽  
Marine Riser ◽  
Highly Nonlinear ◽  
Rectangular Coordinates

A method of static analysis for a marine riser experiencing large displacements is presented. The method is suitable for analyzing a riser having a known top tension and a possible slippage at the top slip joint. Utilizing the stationary condition of a functional coupled with an equilibrium equation, one can conveniently obtain the equilibrium configuration numerically. The configuration is expressed in terms of the rectangular coordinates. The functional representing the energy and work of the riser system is expressed in terms of the horizontal coordinate which is parameterized in terms of the vertical depth instead of arc length. For a two-dimensional problem, two multipliers must be included in the functional. One of the two represents the variable axial force along the length of the riser and the other corresponds to the strain energy per unit riser length due to bending. Utilizing the finite element method, a numerical procedure to obtain the configuration of static equilibrium is given. The resulting algebraic equations are highly nonlinear and the Newton-Raphson iterative procedure is used to solve the equations. An example is given.

Controlling Bifurcation and Dynamic Behavior in Vibro-Impact System

2014 ◽  
Author(s):  
Chi-Wei Kuo ◽  
C. Steve Suh
Keyword(s):  
Dynamic Instability ◽  
Spectral Response ◽  
Sampling Rate ◽  
Working Environment ◽  
Phase Portraits ◽  
Least Mean Square ◽  
Time Step ◽  
Grazing Bifurcation ◽  
Impact System ◽  
Highly Nonlinear

Impact oscillators are found in many applications. Some of the applications inadvertently experience the undesirable effect of vibro-impact called grazing bifurcation. For example, fitting joints are commonly considered in mechanical design. However, the grazing behavior of a loose fitting joint in response to the thermal variation of the working environment may cause unpredictable damage. In this paper, the Newtonian model of a vibro-impact system is investigated. The model system exhibits complex grazing dynamics that is highly nonlinear. The generation of grazing phenomena along with the corresponding periodic solution of the particular type of bifurcation is elaborated. The system is characterized using phase portraits. Since grazing and route-to-chaos are difficult to control, a novel concept capable of simultaneous control of vibration amplitude in the time-domain and spectral response in the frequency-domain is applied to develop a viable control scheme. The concept has been demonstrated working well for the control of dynamic instability including bifurcation and chaos in many engineering systems. The developed controller explores wavelet adaptive filters and filtered-x least mean square algorithm to the successful mitigation of the various states of dynamic instability of the vibro-impact system including grazing bifurcation and chaotic response. In addition, detail description is also given as to the setting of the control parameters such as control time step, sampling rate, wavelet filter vector, and desired targets.

scholarly journals INDEX INSURANCE DESIGN

2019 ◽  
Vol 49 (2) ◽  
pp. 491-523
Author(s):  
Jinggong Zhang ◽  
Ken Seng Tan ◽  
Chengguo Weng
Keyword(s):  
Numerical Procedure ◽  
Optimal Solution ◽  
Utility Functions ◽  
Index Insurance ◽  
Linear Type ◽  
Weather Index ◽  
Basis Risk ◽  
Temperature And Precipitation ◽  
General Utility ◽  
Highly Nonlinear

AbstractIn this article, we study the problem of optimal index insurance design under an expected utility maximization framework. For general utility functions, we formally prove the existence and uniqueness of optimal contract and develop an effective numerical procedure to derive the optimal solution. For exponential utility and quadratic utility functions, we obtain analytical expression of the optimal indemnity function. Our results show that the indemnity can be a highly nonlinear and even non-monotonic function of the index variable in order to align with the actual loss variable so as to achieve the best reduction in basis risk. Due to the generality of model setup, our proposed method is readily applicable to a variety of insurance applications including index-linked mortality securities, weather index agriculture insurance, and index-based catastrophe insurance. Our method is illustrated by numerical examples where weather index insurance is designed for protection against the adverse rice yield using temperature and precipitation as the underlying indices. Numerical results show that our optimal index insurance significantly outperforms linear-type index insurance contracts in terms of basis risk reduction.

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