Intercepting maneuvering target with specified impact angle by modified SDRE technique

A guidance law derived by modifying state dependent Riccati equation technique, to enable the imposition of a predetermined terminal intercept angle to a maneuvering target, is presented in this paper. The interceptor is assumed to have no knowledge about the type of maneuver the target is executing. The problem is cast in a non-cooperative game theoretic form. The guidance law obtained is dependent on the LOS angular rotational rate and on the impact angle error. Theoretical conditions which guarantee existence of solutions under this method have been derived. It is shown that imposing the impact angle constraint calls for an increase in the gains of the guidance law considerably, subsequently requiring a higher maneuverability advantage of the interceptor. The performance of the proposed guidance law is studied using a non-linear two dimensional simulation of the relative kinematics, assuming first order dynamics for the interceptor and target.

Bearing capacity of circular footings over rock mass by using axisymmetric quasi lower bound finite element limit analysis

The ultimate bearing capacity of a circular footing, placed over rock mass, is evaluated by using the lower bound theorem of the limit analysis in conjunction with finite elements and nonlinear optimization. The generalized Hoek-Brown (HB) failure criterion, but by keeping a constant value of the exponent, alpha = 0.5, was used. The failure criterion was smoothened both in the meridian and pi planes. The nonlinear optimization was carried out by employing an interior point method based on the logarithmic barrier function. The results for the obtained bearing capacity were presented in a non-dimensional form for different values of GSI, m(i), sigma(ci)/(gamma b) and q/sigma(ci). Failure patterns were also examined for a few cases. For validating the results, computations were also performed for a strip footing as well. The results obtained from the analysis compare well with the data reported in literature. Since the equilibrium conditions are precisely satisfied only at the centroids of the elements, not everywhere in the domain, the obtained lower bound solution will be approximate not true. (C) 2015 Elsevier Ltd. All rights reserved.

Reply to Discussion on ``Bearing capacity of circular footings over rock mass by using axisymmetric quasi lower bound finite element limit analysis'' Comput. Geotech. 70 (2015) 138-149]

A discussion has been provided for the comments raised by the discusser (Clausen, 2015)1] on the article recently published by the authors (Chakraborty and Kumar, 2015). The effect of exponent alpha for values of GSI approximately smaller than 30 becomes more critical. On the other hand, for greater values of GSI, the results obtained by the authors earlier remain primarily independent of alpha and can be easily used. (C) 2015 Elsevier Ltd. All rights reserved.

Iterative method using consistent mass matrix in axisymmetrical finite element analysis of hypervelocity impact

We present in this paper an iterative method using consistent mass matrix in axisymmetrical finite element analysis of hypervelocity impact. To retain the advantage of integration on an element-by-element basis which is at the heart of modern hydrocodes, we suggest that the first step should be to solve for accelerations at an advanced time step by using the lumped mass approach, then iterate using a consistent mass matrix to improve the estimate. Examples are given to show the improved resolution with the new method.

The application of B-P constitutive equations in finite element analysis of high velocity impact

We present in this paper the application of B-P constitutive equations in finite element analysis of high velocity impact. The impact process carries out in so quick time that the heat-conducting can be neglected and meanwhile, the functions of temperature in equations need to be replaced by functions of plastic work. The material constants in the revised equations can be determined by comparison of the one-dimensional calculations with the experiments of Hopkinson bar. It can be seen from the comparison of the calculation with the experiment of a tungsten alloy projectile impacting a three-layer plate that the B-P constitutive equations in that the functions of temperature were replaced by the functions of plastic work can be used to analysis of high velocity impact.

Otimização de torre de aço para aerogerador eólico.

Diversas formas de geração de energia vêm sendo desenvolvidas com o objetivo de oferecer alternativas ecologicamente corretas. Neste contexto, a energia eólica vem se destacando na região Nordeste do Brasil, devido ao grande potencial dos ventos da região. As torres, que representam parcela significativa do custo total do sistema, tendem a crescer buscando ventos mais fortes e permitindo assim a utilização de aerogeradores com maior capacidade de geração de energia. Este trabalho tem como objetivo formular um modelo de otimização de torres tubulares de aço, para aerogeradores eólicos. Busca-se minimizar o volume total (custo, indiretamente), tendo como variáveis de projeto as espessuras da parede da torre. São impostas restrições relativas à frequência natural e ao comportamento estrutural (tensão e deslocamento máximo de acordo com recomendações da norma Europeia). A estrutura da torre é modelada com base no Método dos Elementos Finitos e o carregamento atuante na estrutura inclui os pesos da torre, do conjunto de equipamentos instalados no topo (aerogerador), e o efeito estático da ação do vento sobre a torre. Para verificação das tensões, deslocamentos e frequências naturais, foram utilizados elementos finitos de casca disponíveis na biblioteca do programa de análise ANSYS. Os modelos de otimização foram também implementados no modulo de otimização do programa ANSYS (design optimization), que utiliza técnicas matemáticas em um processo iterativo computadorizado até que um projeto considerado ótimo seja alcançado. Nas aplicações foram usados os métodos de aproximação por subproblemas e o método de primeira ordem. Os resultados obtidos revelam que torres para aerogeradores merecem atenção especial, em relação à concepção do projeto estrutural, sendo que seu desempenho deve ser verificado através de metodologias completas que englobem além das análises clássicas (estáticas e dinâmicas), incluam também as análises de otimização.

Energy stable and momentum conserving hybrid finite element method for the incompressible Navier-Stokes equations

A hybrid method for the incompressible Navier-Stokes equations is presented. The method inherits the attractive stabilizing mechanism of upwinded discontinuous Galerkin methods when momentum advection becomes significant, equal-order interpolations can be used for the velocity and pressure fields, and mass can be conserved locally. Using continuous Lagrange multiplier spaces to enforce flux continuity across cell facets, the number of global degrees of freedom is the same as for a continuous Galerkin method on the same mesh. Different from our earlier investigations on the approach for the Navier-Stokes equations, the pressure field in this work is discontinuous across cell boundaries. It is shown that this leads to very good local mass conservation and, for an appropriate choice of finite element spaces, momentum conservation. Also, a new form of the momentum transport terms for the method is constructed such that global energy stability is guaranteed, even in the absence of a pointwise solenoidal velocity field. Mass conservation, momentum conservation, and global energy stability are proved for the time-continuous case and for a fully discrete scheme. The presented analysis results are supported by a range of numerical simulations. © 2012 Society for Industrial and Applied Mathematics.

Efficient parametric uncertainty analysis within the hybrid Finite Element/Statistical Energy Analysis method

This paper is concerned with the development of efficient algorithms for propagating parametric uncertainty within the context of the hybrid Finite Element/Statistical Energy Analysis (FE/SEA) approach to the analysis of complex vibro-acoustic systems. This approach models the system as a combination of SEA subsystems and FE components; it is assumed that the FE components have fully deterministic properties, while the SEA subsystems have a high degree of randomness. The method has been recently generalised by allowing the FE components to possess parametric uncertainty, leading to two ensembles of uncertainty: a non-parametric one (SEA subsystems) and a parametric one (FE components). The SEA subsystems ensemble is dealt with analytically, while the effect of the additional FE components ensemble can be dealt with by Monte Carlo Simulations. However, this approach can be computationally intensive when applied to complex engineering systems having many uncertain parameters. Two different strategies are proposed: (i) the combination of the hybrid FE/SEA method with the First Order Reliability Method which allows the probability of the non-parametric ensemble average of a response variable exceeding a barrier to be calculated and (ii) the combination of the hybrid FE/SEA method with Laplace's method which allows the evaluation of the probability of a response variable exceeding a limit value. The proposed approaches are illustrated using two built-up plate systems with uncertain properties and the results are validated against direct integration, Monte Carlo simulations of the FE and of the hybrid FE/SEA models. © 2013 Elsevier Ltd.