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1 – 10 of over 2000This paper extends the linear complementarity problem formulation of [7] and [8] for normal impact of planar deformable bodies in multibody systems. In the kinematics of impact we…
Abstract
This paper extends the linear complementarity problem formulation of [7] and [8] for normal impact of planar deformable bodies in multibody systems. In the kinematics of impact we consider the normal gaps between the impacting bodies in terms of the generalized coordinates. Then, the generalized coordinate’s vector is formulated in terms of the impact forces using the 5th order implicit Runge‐Kutta approach RADAU5. Substituting the generalized coordinates in the relation of normal gaps together with the complementarity relations of unilateral contact constraints leads to a linear complementarity problem where its solution results in the solution of the impact problem including impact forces and normal gaps. Then, alternatively another formulation on velocity level based on the 4th order explicit Runge‐Kutta is presented. In the presented approach no coefficient of restitution is used for treatment of energy loss during impact and, instead, the material damping is responsible for energy loss. A good agreement between the results of our approach with the results of FEM for soft planar deformable bodies was shown in [7]. Here, we improve the results for stiff planar deformable bodies and show that with a proper selection of eigenmodes, the results on both position and velocity level approach the precise results of FEM provided that an optimal time step of the integration is chosen. We also investigate the effect of considering material damping and some higher eigenfrequencies on the amount of energy which is dissipated during impact based on our approach.
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H. Saberi Najafi and S.A. Edalatpanah
– The purpose of this paper is to present the efficient iterative methods for solving linear complementarity problems (LCP), using a class of pre-conditioners.
Abstract
Purpose
The purpose of this paper is to present the efficient iterative methods for solving linear complementarity problems (LCP), using a class of pre-conditioners.
Design/methodology/approach
By using the concept of solving the fixed-point system of equations associated to the LCP, pre-conditioning techniques and Krylov subspace methods the authors design some projected methods to solve LCP. Furthermore, within the computational framework, some models of pre-conditioners candidates are investigated and evaluated.
Findings
The proposed algorithms have a simple and graceful structure and can be applied to other complementarity problems. Asymptotic convergence of the sequence generated by the method to the unique solution of LCP is proved, along with a result regarding the convergence rate of the pre-conditioned methods. Finally, a computational comparison of the standard methods against pre-conditioned methods based on Example 1 is presented which illustrate the merits of simplicity, power and effectiveness of the proposed algorithms.
Research limitations/implications
Comparison between the authors' methods and other similar methods for the studied problem shows a remarkable agreement and reveals that their models are superior in point of view rate of convergence and computing efficiency.
Originality/value
For solving LCP more attention has recently been paid on a class of iterative methods called the matrix-splitting such as AOR, MAOR, GAOR, SSOR, etc. But up to now, no paper has discussed the effect of pre-conditioning technique for matrix-splitting methods in LCP. So, this paper is planning to fill in this gap and the authors use a class of pre-conditioners with iterative methods and analyze the convergence of these methods for LCP.
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Binbin Xun, Fushuan Wen and Shulin Tong
The purpose of this paper is to investigate the gaming equilibrium among fossil‐fueled generation companies (GenCos), wind generation companies, the grid company and customers…
Abstract
Purpose
The purpose of this paper is to investigate the gaming equilibrium among fossil‐fueled generation companies (GenCos), wind generation companies, the grid company and customers participating in an emission trading (ET) market and the day‐ahead electricity market.
Design/methodology/approach
The complementarity method is used in this work to obtain the Nash equilibrium. By combining the Karush‐Kuhn‐Tucker (KKT) conditions of each kind of market participants with market clearing and consistency conditions, a mixed linear complementarity problem could be established.
Findings
Simulation results show that: the enforcement of ET could increase the share of generation outputs of wind generation units, and decrease the emissions from fossil‐fueled generation units; the bilateral contracts between GenCos and customers could limit the ability of exercising market power by GenCos; and when the emissions allowances allocated by the government shrink, the price of emissions allowance will increase and as the result the dispatching order of fossil‐fueled generation units will change, and the shares of generation outputs from wind generation units and combined‐cycle gas turbines increase. However, it should be mentioned that because the cost of wind generation is still very high, the increase of the share from wind generation units in the electricity market should mainly rely on cost reduction rather than the enforcement of ET.
Originality/value
The original contribution and the value of this study lie in developing a model framework to explore the gaming equilibrium that thermal and wind generating plants both play in the emissions trading environment and electricity market.
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Billy Fredriksson, Bo Torstenfelt and Nils Endahl
The importance of contact and friction problems in different application areas is discussed. Methods and algorithms for numerical solutions using the finite element method are…
Abstract
The importance of contact and friction problems in different application areas is discussed. Methods and algorithms for numerical solutions using the finite element method are presented. Both elastic and elastic plastic materials are included as well as combination of contact and crack problems. The methods are applied to practical applications such as bolted joints, lugs and roller bearings.
S. Alliney, A. Strozzi and A. Tralli
A finite element model for the elastohydrodynamic lubrication problem is presented. A coupling between the hydrodynamic equation and the foundation compliance equation is…
Abstract
A finite element model for the elastohydrodynamic lubrication problem is presented. A coupling between the hydrodynamic equation and the foundation compliance equation is performed, then the resulting functional problem is given an ‘extended’ variational formulation. Some preliminary numerical results are also presented.
Wei Wang, Junping Shi, Xiaoshan Cao and Yifeng Hu
The partition of unity of the standard meshless Galerkin method is used as basis in expressing the discontinuity of the contact surface displacement, particularly by adding…
Abstract
Purpose
The partition of unity of the standard meshless Galerkin method is used as basis in expressing the discontinuity of the contact surface displacement, particularly by adding discontinuous terms into the displacement mode, and constructing the discontinuous meshless displacement field function. In this study the contact surface equation is aimed to derive from the improved Coulomb friction contact model.
Design/methodology/approach
In this paper based on the basic idea of meshless method, an improved moving least squares approximation function (expansion method based on out of unit division) is applied to the analysis of two-dimensional contact problems.
Findings
On the basis of this equation after discrete processing, it is combined with the discrete form of the virtual work equation with added contact conditions, and eventually transformed into a standard linear complementary problem. Moreover, it is solved by using the Lemke algorithm, and a corresponding example is provided in this research.
Originality/value
The proposed method can effectively control the mutual embedding of the contact surface, and the stress distribution that is the same as the actual situation can be obtained on the contact surface.
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This contribution discusses a continuum model of large discrete networks in planar domains. For this model, the Kirchhoff law, boundary conditions and capacity constraints lead in…
Abstract
This contribution discusses a continuum model of large discrete networks in planar domains. For this model, the Kirchhoff law, boundary conditions and capacity constraints lead in a system optimisation approach to a infinite dimensional constrained optimisation problem and to “mixed” variational inequalities. Mixed finite element methods can be formulated for these variational inequalities such that computable discretizations of the continuum problem are obtained.
Mahmood Khaksar-e Oshagh, Mostafa Abbaszadeh, Esmail Babolian and Hossein Pourbashash
This paper aims to propose a new adaptive numerical method to find more accurate numerical solution for the heat source optimal control problem (OCP).
Abstract
Purpose
This paper aims to propose a new adaptive numerical method to find more accurate numerical solution for the heat source optimal control problem (OCP).
Design/methodology/approach
The main aim of this paper is to present an adaptive collocation approach based on the interpolating wavelets to solve an OCP for finding optimal heat source, in a two-dimensional domain. This problem arises when the domain is heated by microwaves or by electromagnetic induction.
Findings
This paper shows that combination of interpolating wavelet basis and finite difference method makes an accurate structure to design adaptive algorithm for such problems which usually have non-smooth solution.
Originality/value
The proposed numerical technique is flexible for different OCP governed by a partial differential equation with box constraint over the control or the state function.
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This paper is the description of a new two‐grid algorithm tosolve frictional contact problems. A regularized formulation is introducedand the discretized problem is solved using…
Abstract
This paper is the description of a new two‐grid algorithm to solve frictional contact problems. A regularized formulation is introduced and the discretized problem is solved using an internal non linear two‐grid technique coupled with a diagonal fixed point algorithm. Mathematical background is given, and superconvergence is obtained.
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