Sharif Digital Repository

This paper presents the dynamic modeling and design of micro motion compliant parallel mechanism with flexible intermediate links and rigid moving platform. Modeling of mechanism is described with closed kinematic loops and the dynamic equations are derived using Lagrange multipliers and Kane's methods. Euler-Bernoulli beam theory is considered for modeling the intermediate flexible link. Based on the Assumed Mode Method theory, the governing differential equations of motion are derived and solved using both Runge-Kutta- Fehlberg4, 5th and Perturbation methods. The mode shapes and natural frequencies are calculated under clamped-clamped boundary conditions. Comparing perturbation method with... 

In this paper, a new algorithm for solving constrained nonlinear programming problems is presented. The basis of our proposed algorithm is none other than the necessary and sufficient conditions that one deals within a discrete constrained local optimum in the context of the discrete Lagrange multipliers theory. We adopt a revised particle swarm optimization algorithm and extend it toward solving nonlinear programming problems with continuous decision variables. To measure the merits of our algorithm, we provide numerical experiments for several renowned benchmark problems and compare the outcome against the best results reported in the literature. The empirical assessments demonstrate that... 

In this work, numerical simulation is used to study the stability enhancement of high speed supercavitating Shkval missile. Although supercavitation is known as one of the most effective methods for drag reduction, producing the cavity, either by ventilation or by cavitator at front of the body, may cause some instabilities on cavity surface and thus on the projectile's motion. Therefore removing these instabilities comes as an important point of discussion. First of all, we calculate the sources of instabilities and measure respective forces and then present some approaches that significantly reduce these instabilities. One of these methods that could produce more stable supercavities is... 

In this paper, a new multi-scale technique is developed for concurrent coupling of atomistic-continuum domains in modeling nano-mechanical behavior of atomic structures. A Lagrange multiplier method is employed over an overlapping domain to coupling the continuum nodal velocities with atomic lattice velocities. The Hamiltonian method is applied to combine the continuum and molecular Hamiltonians with the same weight in the overlapping domain. The mass and stiffness matrices of the continuum domain are obtained using a linear bridging map of the atomic lattice displacement laid underneath the continuum grid to the element displacements. Numerical examples are performed by presenting the... 

In this paper, a general class of Eshelby-like or weighted stress tensors based on the right stretch tensor is defined as the product of a general type of Lagrangian stress tensor and a class of stretch measure. In addition, basis free relations for conjugate strains of Eshelby-like stress tensors are investigated, which are based on Hill's definition of energy conjugacy. The equations for strain tensors conjugate to Eshelby-like stress tensors are generally determined, but the case in which the conjugate strains are coaxial with the right stretch tensor is mostly investigated. © 2006 Elsevier Ltd. All rights reserved  

In this paper, we introduce a new method and new motion variables to study kinematics and dynamics of a 6 d.o.f cable-driven robot. Using these new variables and Lagrange equations, we achieve new equations of motion which are different in appearance and several aspects from conventional equations usually used to study 6 d.o.f cable robots. Then, we introduce a new Jacobian matrix which expresses kinematical relations of the robot via a new approach and is basically different from the conventional Jacobian matrix. One of the important characteristics of the new method is computational efficiency in comparison with the conventional method. It is demonstrated that using the new method instead... 

A major disadvantage of conventional meshless methods as compared to finite element method (FEM) is their weak performance in dealing with constraints. To overcome this difficulty, the penalty and Lagrange multiplier methods have been proposed in the literature. In the penalty method, constraints cannot be enforced exactly. On the other hand, the method of Lagrange multiplier leads to an ill-conditioned matrix which is not positive definite. The aim of this paper is to boost the effectiveness of the conventional reproducing kernel particle method (RKPM) in handling those types of constraints which specify the field variable and its gradient(s) conveniently. Insertion of the gradient term(s),... 

In this work, numerical simulation is used to study the stability enhancement of high speed supercavitating Shkval missile. Although supercavitation is known as one of the most effective methods for drag reduction, producing the cavity, either by ventilation or by cavitator at front of the body, may cause some instabilities on cavity surface and thus on the projectile's motion. Therefore removing these instabilities comes as an important point of discussion. First of all, we calculate the sources of instabilities and measure respective forces and then present some approaches that significantly reduce these instabilities. One of these methods that could produce more stable supercavities is... 

In this paper the effect of thrust on the bending behaviour of flexible missiles is investigated. For this purpose, the governing equations of motion of a flexible guided missile are derived following the Lagrangian approach. The missile is idealized as a non-uniform beam where the bending elastic deflections are modelled using the method of modal substitution. The vehicle (time varying) bending modeshapes and natural frequencies are determined by modelling variable mass and stiffness distributions with thrust and mass burning effects accounted for. To solve this problem the missile is divided into several segments of uniform stiffness, density and axial force distribution. This approach... 

In this study, the dynamic response of the laminated composite beam with arbitrary lay-ups has been investigated within the framework of the third-order shear deformation theory using the finite element method. A new three-nodded finite element compliant with the theory is introduced next. To deal with the dynamic contact between the delaminated segments, unilateral contact constraints are employed in conjunction with Lagrange multiplier method. Furthermore, the Poisson's effect is incorporated in the formulation of the beam constitutive equation. Also, the higher-order inertia effects and material couplings (flexure-tensile, flexure-twist and tensile-twist couplings) are considered in the... 

This paper studies a brachiation robot that is a long armed locomotion similar to apes. The robot has 2 revolute joints but only one of them is actuated. In this paper, after deriving dynamic model of the robot the Controlled Lagrangian (CL) method is used for stabilization. The matching conditions satisfied for the controller are derived and the extended λ-method is used to solve PDE's involved in the method of controlled lagrangian. Satisfactory controller's gains are chosen by PSO algorithm. Finally, feasibility of the developed controller is investigated by numerical simulations  

Facility location problem is one of the strategic logistical drivers within the supply chain which is a hard to solve optimization problem. In this study, we focus on the uncapacitated single-source multi-product production/ distribution facility location problem with the presence of set-up cost. To efficiently tackle this decision problem, two Lagrangian-based heuristics are proposed one of which incorporates integer cuts to strengthen the formulation. Local search operators are also embedded within these methods to improve the upper bounds as the search progresses. Three sets of instances with various characteristics are generated and used to evaluate the performance of the proposed... 

In this study, the issue of allocating the cost of transient stability relief in a bilateral electricity market is investigated. The results of a constrained generation scheduling problem can be utilised in two ways to price the cost of a constraint. In the first method, which is the basis of nodal pricing, the Lagrange multipliers of the nodal power balance constraint are used as the price of electricity at various buses. In the second method, which is used in this study, the constraint relief scheme is based on a bid-based adjustment market of increments and decrements offered by generators to be involved in the constraint relief process. In the scheme used in this study, the cost of... 

A new method for structural optimization is presented for successive approximation of the objective function and constraints in conjunction with Lagrange multipliers approach. The focus is on presenting the methodology with simple examples. The basis of the iterative algorithm is that after each iteration, it brings the approximate location of the estimated minimum closer to the exact location, gradually. In other words, instead of the linear or parabolic term used in Taylor expansion, which works based on a short step length, an arch is used that has a constant curvature but a longer step length. Using this approximation, the equations of optimization involve the Lagrange multipliers as the... 

The main focus of this study is on reserve market settlement in an electricity market with marginal pricing scheme as the pricing mechanism. Following a day-ahead market clearing, the marginal prices are found using the appropriate Lagrange multipliers as the bi-products of the optimisation process. The payments to energy and reserve providers can then be found based on these prices. However, it is hard to find an appropriate settlement scheme that provides the fair and justifiable consumer payments based on marginal pricing scheme considering the actual reserve functions in power systems. In this study, a reserve marginal pricing that is based on a proper reserve marginal price definition... 

BIBO stability of linear time-invariant (LTI) distributed order dynamic systems with non-negative weight functions is investigated in this paper by using Lagrange inversion theorem. New sufficient conditions of stability/instability are presented for these systems accordingly. These algebraically simple conditions are relatively tight and their conservatism is adjustable. © 2018 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd  

In this paper we investigate the Shannon capacity of single and parallel Poisson channels in different scenarios. At first, by examining the capacity equation of the single Poisson channel, the minimum average power that maximizes the capacity is found. Then, applying the method of Lagrange multipliers on the capacity expression of the parallel Poisson channel, we obtain the optimum power allocation maximizing the parallel Poisson channel capacity  

The maximally flat (MF) fractional delay (FD) filter which is in fact a Lagrange interpolator for uniformly sampled signals, has previously been shown to be equal to the scaled binomially windowed shifted version of the sinc function; the ideal interpolation kernel for band-limited signals. In this paper, another proof for this equivalence is presented. Unlike its counterparts available in the literature, the proof given here is neither strictly algebraic, nor deploys the explicit coefficient formulas of the MFFD filter. It follows a frequency domain approach based on the definition of this filter instead, and aims to provide more insight into the corresponding equivalence. © 2009 Elsevier... 

In this paper, a Lagrangian-extended finite-element (FE) method is presented in modeling large-plasticity deformations and contact problems. The technique is used to model arbitrary interfaces in two-dimensional (2D)/three-dimensional (3D) large deformations. The material interfaces are represented independent of the FE mesh and the process is accomplished by integrating enriched elements with a larger number of Gauss points, whose positions are fixed in the element. The large elasto-plastic deformation formulation is employed within the eXtended Finite-Element Method (X-FEM) framework to simulate the nonlinear behavior of materials. The interface between two bodies is modeled by using the... 

The accomplishment of design for devices and applications such as cloaking has been feasible using transformation optics. This feasibility has been extended to the design of cloaks for concave bodies. Even though the process of cloaking in concave shaped bodies has been addressed in literature, the problem of poor accuracy and poor quality of cloaking remains. In accordance with the aim to outmanoeuvre the problem, the surface of interest which could be of convex or concave nature is modelled using a piecewise higher order parametric function. This function is expressed using Lagrange's interpolation. The calculation of piecewise model involves the inversion of the Lagrangian polynomial. But...