1,721,150 research outputs found
A methodology for the generation of low-cost higher-order methods for linear dynamics
No full textThis work presents a methodology which generates efficient higher-order methods for linear dynamics by improving the accuracy properties of Norsett methods towards those of Pade methods. The methodology is based on a simple and low-cost iterative procedure which is used to implement a set of higher-order methods with controllable dissipation. A sequence of improved solutions is obtained which correspond to algorithms offering an effective compromise between the efficiency of Norsett methods and the accuracy of Pade methods. Moreover, a direct control over high-frequency dissipation is possible by means of an algorithmic parameter. Numerical tests are reported which confirm that this set of algorithms is really attractive for linear dynamic analysis. Copyrigh
Collocation methods with controllable dissipation for linear dynamics
No full textThis paper introduces a unified set of collocation methods for linear dynamics in which a parameter is used to control the position of the collocation points. In this manner, both A-stable algorithms of order 2p and L-stable algorithms of order 2p - 1 are derived from collocation polynomials of degree p. In addition, algorithms with intermediate accuracy and stability properties are made available. The effects of varying the algorithmic parameter are investigated with particular reference to the numerical dissipation of spurious high-frequency modes. Numerical tests are reported which support the theoretical analysis and demonstrate the performance of the proposed algorithms. (C) 2001 Elsevier Science B.V. All rights reserved
An efficient time discontinuous Galerkin procedure for non-linear structural dynamics
No full textThis paper presents an effective time discontinuous Galerkin procedure for non-linear dynamics. The procedure is based on a cheap iterative algorithm, which is rather different from previous efforts. In fact, the algorithm is designed so that the corrected solutions inherit the desired stability and dissipative properties and the iterations serve only to improve accuracy. Some numerical tests illustrate the good performance of the present procedure, which appears to be competitive with the available implementations of time discontinuous Galerkin methods
The Norsett time integration methodology for finite element transient analysis
No full textThis paper presents a set of methods for time integration of problems arising from finite element semidiscretizations. The purpose is to obtain computationally efficient methods which possess higher-order accuracy and controllable dissipation in the spurious high modes. The methods are developed and analysed by a general collocation methodology which leads to the class of Norsett approximants. An algorithmic parameter is used to achieve an effective control over numerical dissipation. Moreover, a simple and efficient implementation scheme is presented. At each time step, algorithms based on p-order collocation polynomials require the solution of p sets of linear algebraic equations with the same coefficient matrix. In this way, a single factorization is needed and no transformations are required to recover the approximate solution at the end or within the time interval. To demonstrate the performance of the proposed algorithms, a wide experimental evaluation is carried out on typical test problems in finite element transient analysis. (C) 2002 Elsevier Science B.V. All rights reserved
An efficient integration procedure for linear dynamics based on a time discontinuous Galerkin formulation
No full textThis work presents an effective procedure devised to implement the time discontinuous Galerkin method for linear dynamics. In particular, the method with piecewise linear time interpolation is considered. The procedure is based on a simple and low-cost iterative scheme, which is designed not as a mere solution algorithm, but rather as a method to generate improved approximations to the exact solution. The corrected solutions inherit the desired stability and dissipative properties from the target solution, while accuracy is improved by iterations. Indeed, no more than two iterations are shown to be needed. The resultant algorithm leads to remarkable computational savings and can be easily implemented into existing finite element codes. Numerical tests confirm that the present procedure possesses many attractive features for applications to dynamic analysis
Consistency and recovery in electroelasticity Part I: Standard finite elements
No full textDeveloping finite elements for electroelastic analysis requires a special care as the coupling in the discrete equations depends on the matching between the approximations assumed for mechanical and electrical variables. To provide a formal basis to this intuitive remark, a notion of consistency is established and a rigorous consistency analysis is presented for the standard finite element model based on assumed displacement and electric potential. In this way, specific analytical requirements are obtained which serve as a guide to select the interpolation functions for primary variables. Moreover, the analysis shows that violating consistency can be reflected as spurious outcomes upsetting the local distributions of secondary variables. Indeed, this undesirable effect is shown to be typical of the standard approach if stress and electric flux density are computed via the constitutive equations. To cure the trouble, an alternative recovery procedure is devised based on the consistency analysis. The procedure is variationally correct and reconstitutes in a consistent manner the distributions of stress and electric flux density. © 2002 Elsevier Science B.V. All rights reserved
On the consistency of finite element models in thermoelastic analysis
No full textIn thermoelastic analysis, compatible finite elements may predict oscillating stresses if the temperature distribution is not coherent with the element strain coming from the assumed displacement approximation. Modelling the stress field as an independent variable could be a viable alternative to avoid these spurious outcomes. To this purpose, the behavior of mixed, hybrid stress and equilibrium finite element models in the presence of initial strains due to temperature is investigated and compared with the usually employed displacement approach. The consistency requirement for each model is established and the spurious outcomes due to inconsistent temperature fields are discussed, examining also the effects of element geometry distortions. The analysis, illustrated through some numerical tests, shows that a direct approximation for the stress field can eliminate, or at least reduce, the generation of spurious stress modes, although this is not a priori guaranteed by a mixed approach. © 2001 Elsevier Science B.V. All rights reserved
Recovery of consistent stresses for compatible finite elements
No full textIn displacement based finite element models, stresses deduced directly from the constitutive relationship can show local erratic behaviour. This occurs in problems involving initial stresses or strains, or varying rigidities over the element domain, when local stresess do not meet a specific consistency requirement. In this context, an integrated procedure for recovering consisten stresses, that is stresses riddled of spurious outcomes, is proposed. The procedure is developed within a general weighted residual approach, suitably specialized for the purpose. The relationship between the proposed procedure and those based on the Hu-Washizu formulation is also elucidated. For illustration purpose, some numerical tests are included. © 2002 Elsevier Science B.V. All rights reserved
A new smart sustainable earth-cement composite doped by carbon microfibers with self-sensing properties
No full textCivil constructions need to be monitored during their lifespan to assess any changes in structural performance following critical events. Among the various available monitoring solutions, this paper contributes to the literature on multifunctional construction materials that have the ability to provide an electrical output that can be correlated with materials’ damage. The novelty of the work consists of achieving self-sensing properties in a sustainable concrete, where cement is substituted with natural earth in the ratio of 7/2 in volume. Self-sensing properties are provided through the addition of a small amount of carbon microfibers enabling a piezoresistive behavior. Experimental tests were carried out using samples with different shapes to investigate their electrical and sensing properties. The results showed that the best carbon microfiber doping level of 0.05% relative to the binder exhibited clear and repeatable signals, an average gauge factor of 46, and high linearity. Moreover, the smart multifunctional earth-concrete showed good electrical, diagnostic, and sensing properties during failure tests
Time continuous Galerkin methods for linear heat conduction problems
No full textA Petrov-Galerkin formulation of the semidiscrete linear transient heat conduction problem is given, from which a unified set of A-stable higher-order time integration methods is derived. Accuracy and stability properties can be controlled by an algorithmic parameter introduced in the definition of the test functions. In this manner. A-stable algorithms of order 2p and L-stable algorithms of order 2p - 1 are derived from a unique formulation. In addition, algorithms with intermediate accuracy and stability properties are made available. The effects of varying the algorithmic parameter are investigated. Numerical tests are included to support the theoretical analysis. (C) 2000 Elsevier Science S.A. All rights reserved
- …
