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When simulating fluid-structure interaction (FSI), it is often essential that the no-slip condition is accurately enforced at the wetted boundary of the structure. This paper aims to evaluate the relative strengths and limitations of the penalty and Lagrange multiplier methods, within the context of modelling FSI, through a comparative analysis.

In the immersed boundary method, the no-slip condition is typically imposed by augmenting the governing equations of the fluid with an artificial body force. The relative accuracy and computational time of the penalty and Lagrange multiplier formulations of this body force are evaluated by using each to solve three test problems, namely, flow through a channel, the harmonic motion of a cylinder through a stationary fluid and the vortex-induced vibration (VIV) of a cylinder.

The Lagrange multiplier formulation provided an accurate solution, especially when enforcing the no-slip condition, and was robust as it did not require “tuning” of problem specific parameters. However, these benefits came at a higher computational cost relative to the penalty formulation. The penalty formulation achieved similar levels of accuracy to the Lagrange multiplier formulation, but only if the appropriate penalty factor was selected, which was difficult to determine a priori.

Both the Lagrange multiplier and penalty formulations of the immersed boundary method are prominent in the literature. A systematic quantitative comparison of these two methods is presented within the same computational environment. A novel application of the Lagrange multiplier method to the modelling of VIV is also provided.

The purpose of this paper is to present the benefits of using the Lagrangian relaxation (LR) and subgradient methods in scenario studies for wavelength division multiplexing (WDM) network planning. The problem of WDM network planning for a given set of lightpath demands in a mesh topology network is to select lightpath routes and then allocate wavelength channels to the lightpaths. In WDM network planning, a scenario study is to find out the network performance under different lightpath demands and/or different network resource configurations.

A scenario study must solve a series of related static WDM network planning problems. Each static WDM network planning problem is an optimization problem, and may be formulated as an integer linear programming problem, which can be solved by the proposed Lagrangian relaxation and subgradient methods. This paper uses the Lagrange multipliers that are obtained from previous scenarios as initial Lagrange multiplier values for other related scenarios.

This approach dramatically reduces the computation time for related scenarios. For small to medium variations of scenarios, the method reduces the computation time by several folds. The proposed method is the first method that effectively considers the relations between related scenarios, and uses such relations to improve the computation efficiency of scenario studies in WDM network planning.

The method improves the efficiency of a scenario study in WDM network planning. By using it, many “what‐if” type of scenario study questions can be answered quickly.

Unlike other existing methods that treat each scenario individually, this method effectively uses the information of the relation between different scenarios to improve the overall computation efficiency.

The purpose of this paper is to propose a combined reordering scheme with a wide range of application, called Reversed Cuthill-McKee-approximate minimum degree (RCM-AMD), to improve a preconditioned general minimal residual method for solving equations using Lagrange multiplier method, and facilitates the choice of the reordering for the iterative method.

To reordering the coefficient matrix before a preconditioned iterative method will greatly impact its convergence behavior, but the effect is very problem-dependent, even performs very differently when different preconditionings applied for an identical problem or the scale of the problem varies. The proposed reordering scheme is designed based on the features of two popular ordering schemes, RCM and AMD, and benefits from each of them.

Via numerical experiments for the cases of various scales and difficulties, the effects of RCM-AMD on the preconditioner and the convergence are investigated and the comparisons of RCM, AMD and RCM-AMD are presented. The results show that the proposed reordering scheme RCM-AMD is appropriate for large-scale and difficult problems and can be used more generally and conveniently. The reason of the reordering effects is further analyzed as well.

The proposed RCM-AMD reordering scheme preferable for solving equations using Lagrange multiplier method, especially considering that the large-scale and difficult problems are very common in practical application. This combined reordering scheme is more wide-ranging and facilitates the choice of the reordering for the iterative method, and the proposed iterative method has good performance for practical cases in in-house and commercial codes on PC.

This study considers a Lagrange direct way of modal assurance criterion (MAC) values of an undamped system. The mentioned method for the sensitivity analysis of the MAC of a sliding machine working table is more close to the exact solution and time efficient. The paper aims to discuss these issues.

Using the Lagrange multipliers to compute the first and second-order sensitivity analysis of MAC values.

Because of the Lagrange multiplier without considering the number of design parameters, one only needs to perform the calculation once. Compared with the indirect way, the direct way is more effective when the number of design parameters is greater than one. This calculation procedure is simple and accurate, which can be popularized and used.

Engineering structure often requires only some structure design, and most of the sub-structure design variables are not related to each other. In this case, this way is better and more efficient. The direct way can be applied to the dynamic optimization design of large structures, the frequency and the mode sensitivity analysis in the process of model modification.

The purpose of this paper is to propose an efficient iterative method for large-scale finite element equations of bad numerical stability arising from deformation analysis with multi-point constraint using Lagrange multiplier method.

In this paper, taking warpage analysis of polymer injection molding based on surface model as an example, the performance of several popular Krylov subspace methods, including conjugate gradient, BiCGSTAB and generalized minimal residual (GMRES), with diffident Incomplete LU (ILU)-type preconditions is investigated and compared. For controlling memory usage, GMRES(m) is also considered. And the ordering technique, commonly used in the direct method, is introduced into the presented iterative method to improve the preconditioner.

It is found that the proposed preconditioned GMRES method is robust and effective for solving problems considered in this paper, and approximate minimum degree (AMD) ordering is most beneficial for the reduction of fill-ins in the ILU preconditioner and acceleration of the convergence, especially for relatively accurate ILU-type preconditioning. And because of concerns about memory usage, GMRES(m) is a good choice if necessary.

In this paper, for overcoming difficulties of bad numerical stability resulting from Lagrange multiplier method, together with increasing scale of problems in engineering applications and limited hardware conditions of computer, a stable and efficient preconditioned iterative method is proposed for practical purpose. Before the preconditioning, AMD reordering, commonly used in the direct method, is introduced to improve the preconditioner. The numerical experiments show the good performance of the proposed iterative method for practical cases, which is implemented in in-house and commercial codes on PC.

This article presents a geometrically non-linear finite element formulation for the analysis of planar two-layer beam-columns taking into account the inter-layer slip and uplift.

The co-rotational method is adopted, in which the motion of the element is decomposed into a rigid body motion and a small deformational one. The geometrically linear formulation can be used in the local frame and automatically be transformed into a geometrically nonlinear one. In co-rotational frame, both layers are assumed to be discretely connected at the element ends. Slips and uplifts are assumed to be small. Consequently, the condition of non interpenetration between the layers can be treated using a node-to-node contact algorithm. The resolution methods such as penalty (PM) and augmented Lagrangian method (ALM) with Uzawa updating scheme can be used.

The non-penetration condition between the layers of composite beams can be formulated by using contact law. It is found that despite a low convergence rate of augmented Lagrangian method compared to penalty method, the former prevents the unrealistic penetration. Besides, it is shown that the buckling load of the composite beam-column is largely affected by the uplift stiffness of the connectors.

The proposed finite element model is capable of simulating accurately the geometrically non-linear behavior of planar two-layer beam-columns taking into account the inter-layer slip and uplift. Regarding uplift, the non-penetration condition is strictly enforced by considering rigorous contact conditions at the interface. The constraint problem is solved using the penalty method or the augmented Lagrangian method with the Uzawa updating scheme.

The purpose of this paper is to present a formulation that couples equivalent plate and beam models for aircraft structures analysis, suitable in conceptual design in which fast model generation and efficient analysis capability are required.

Assembling the complete model with common techniques such as Lagrange multipliers or penalty function method would require a solver capable of handling the combined set of linear equation. The alternative approach proposed here is based on a static reduction of the beam model at specified connection points and the subsequent “embedding” into the equivalent plate model using a coordinate transformation, translating physical dfs in Ritz coordinates, i.e. polynomial coefficients. Displacements and forces on beam elements are recovered with the inverse transformation once the solution is computed.

An aeroelastic trim analysis on a Transonic CRuiser (TCR) civil aircraft conceptual model validates the hybrid model: as the TCR features a slender flexible fuselage and a wide root chord wing, the capability to reduce the beam model for the fuselage at more than one connection point improved aeroelastic corrections to steady longitudinal aerodynamic derivatives.

Although the equivalent model proposed is simpler than others found in literature, it offers automatic mesh generation capabilities, and it is fully integrated into an aeroelastic framework. The hybrid model represents an enhancement allowing both dynamical and static analyses.

The purpose of this paper is to present an application of the simulated annealing algorithm to the redundant system reliability optimization. Its main aim is to analyze and compare this optimization method performance with those of similar application.

The methods that were used to compare results are the genetic algorithm, the Lagrange Multipliers, and the evolution strategy. A hybrid algorithm composed by simulated annealing and genetic algorithm was developed in order to achieve the general applicability of the methods. The hybrid algorithm also tries to exploit the positive aspects of each method.

The results presented by the simulated annealing and the hybrid algorithm are significant, and validate the methods as a robust tool for parameter optimization in mechanical projects development.

The main objective is to propose a method for redundancy optimization in mechanical systems, which are not as large as electric and electronic systems, but involves high costs associated to redundancy and requires a high level of safety standards like: automotive and aerospace systems.

The paper aims to explore the optimal strategies of inventory financing when the risk-averse retailer has different objectives, in the presence of multi-risk, i.e. demand risk, non-operational risk and retailer's strategic default risk.

This paper develops an inventory financing model consisting of a bank and a risk-averse retailer with strategic default. This paper considers two scenarios, i.e. the capital-constrained retailer cares about its profit or firm value. In the first scenario, the bank acts as a Stackelberg leader determining its interest rate, and the retailer acts as a follower determining its pledged quantity. In the second one, the bank capital market is perfectly competitive. Lagrange multiplier method is adopted to solve the optimization.

The optimal strategies in inventory financing scheme in two scenarios are derived. Only when the initial stock is relatively high, the retailer pledges part of the initial stock. Retailer's risk aversion reduces its pledged quantity and performance. The strategic default reduces its profit. When it is relatively high, the bank refuses to offer the loan.

Analytical inventory and financing strategies are specified to help retailers and banks to better understand the interaction of finance and operations management and to better respond to multi-risk.

New results and managerial insights are derived by incorporating partially endogenous strategic default and risk aversion into inventory financing, which enriches the interfaces of operations management and finance.