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Mesolevel simulation of reinforced concrete structures under impact loadings
Published in Günther Meschke, René de Borst, Herbert Mang, Nenad Bićanić, Computational Modelling of Concrete Structures, 2020
Gianluca Cusatis, Daniele Pelessone
The behavior of reinforced concrete structures is greatly influenced by the behavior of the reinforcement and by its coupling with the surrounding concrete matrix. The most common type of reinforcement used in practice has the form of steel rebars. In structural dynamic simulations, rebars are effectively modeled using beam finite elements with strain-rate dependent elasto-plastic constitutive equations for the steel material. Various algorithms have been developed for tying rebars elements to lattice model, as discussed in Pelessone (2005). The rebar-concrete coupling algorithm employed in the simulations described below is the simplest of them and it provides good coupling while simplifying the model generation. The lattice system and the beam finite element mesh simulating the reinforcement (rebars) are independently generated. The particles (aggregate + surrounding mortar) crossed by the rebars are then constrained to the rebar nodes through either a penalty method or a master-slave method. The two constraint algorithms have their own advantages and disadvantages. The penalty method is conceptually simpler and easier to implement. In addition, it also allows, contrarily to the master-slave approach, modeling nonlinear bond slippage at the concrete-rebar interface. The downside of the penalty method is that the rigid constraint holding in the linear elastic regime can be only approximately enforced by setting the penalty constants to very high values. In turn, these constants, which represent the stiffness of the concrete-rebar bond interface may lead to numerical instabilities. The numerical simulations presented in the next sections are carried out by adopting the master-slave approach.
Domain decomposition methods for modelling of deformable block structure
Published in Zikmund Rakowski, Geomechanics 93, 2018
Since more than twenty years, a number of methods have been developed for analysis of stress and deformations of deformable block structure. We can observe two essentially different approaches. The first one is based on using various interface elements. Let us quote Goodman and John (1977) and Desai and others (1984) to give important examples in this line. The advantage of this method is that it is easy to implement and that it can be used to modelling of very complex nonlinear response of the interface. However, from the mathematical point of view, the method may be identified with the penalty method so that is suffers from the well known drawbacks of the latter method.
Real-Time Energy Management Strategies for Buildings and Blocks
Published in Bruno Peuportier, Fabien Leurent, Jean Roger-Estrade, Eco-Design of Buildings and Infrastructure, 2020
Maxime Robillart, Marie Frapin
The principle of penalty methods is to solve a modified optimal control problem whereby a term, called the penalty function, is added to the original cost function. This penalty function presents a divergent behaviour when the constraints are approached by a solution. Penalty methods attempt to approximate a constrained optimal control problem with a series of unconstrained optimal control problems and then apply standard techniques to obtain solutions. Constraint satisfaction is favoured by modifying the cost function and depends on the weight of the penalty functions.
Generalized penalty method for semilinear differential variational inequalities
Published in Applicable Analysis, 2022
Lijie Li, Liang Lu, Mircea Sofonea
Penalty methods represent a mathematical tool used in the study of a large variety of problems, including the analysis and numerical solution of constrained problems. Reference in the field are [13–15], among others. The idea of penalty methods is to construct a sequence of unconstrained problems which have unique solution which converge to the solution of the original constrained problem, as the penalty parameter tends to zero. Penalty methods for variational inequalities have been studied by many authors, mainly for numerical purposes. Details can be found in [16] and the references therein. However, as far as we known, most of references use penalty methods to study only a single variational inequality and very few works are dealing with penalty methods for differential variational inequalities. Among them we refer the reader to the recent papers [17,18]. There, the authors prove existence, uniqueness and convergence results for a penalty method in the study of differential variational inequalities.
Folding behavior of the thin-walled lenticular deployable composite boom: Analytical analysis and many-objective optimization
Published in Mechanics of Advanced Materials and Structures, 2023
Tian-Wei Liu, Jiang-Bo Bai, Nicholas Fantuzzi
Penalty methods are general approaches to solve constraints in optimization problems. However, penalty methods require user-defined problem-dependent parameters, which usually have a negative effect on the performance of the algorithm. Therefore, adaptive penalty techniques [24] have been attracted a great attention. An adaptive penalty technique for dealing with the constraints in optimization problems was employed in this article. A penalty coefficient was set in the fitness function. For any feasible solution, the penalty coefficient was 1; for any unfeasible solution, the penalty coefficient was greater than 1. Moreover, the penalty coefficient was increased with the increased magnitude of the constraint violation.
Network-wide on-line travel time estimation with inconsistent data from multiple sensor systems under network uncertainty
Published in Transportmetrica A: Transport Science, 2018
Hu Shao, William H. K. Lam, Agachai Sumalee, Anthony Chen
The penalty method is one of the most widely used approaches for transforming a constrained optimization problem into an unconstrained one. The penalty method replaces a constrained optimization problem with a series of unconstrained problems whose solutions ideally converge to deliver a solution to the original constrained problem. The unconstrained problems are formed by adding a penalty term to the objective function, which consists of a penalty parameter and a measure of constraint violation. The measure of violation is nonzero when the constraints are violated, and zero in the regions in which they are not.