Chaos-Galerkin solution of stochastic Timoshenko bending problems

This paper presents an accurate and efficient solution for the random transverse and angular displacement fields of uncertain Timoshenko beams. Approximate, numerical solutions are obtained using the Galerkin method and chaos polynomials. The Chaos-Galerkin scheme is constructed by respecting the theoretical conditions for existence and uniqueness of the solution. Numerical results show fast convergence to the exact solution, at excellent accuracies. The developed Chaos-Galerkin scheme accurately approximates the complete cumulative distribution function of the displacement responses. The Chaos-Galerkin scheme developed herein is a theoretically sound and efficient method for the solution of stochastic problems in engineering. (C) 2011 Elsevier Ltd. All rights reserved.

Galerkin Solution of Stochastic Beam Bending on Winkler Foundations

In this paper, the Askey-Wiener scheme and the Galerkin method are used to obtain approximate solutions to stochastic beam bending on Winkler foundation. The study addresses Euler-Bernoulli beams with uncertainty in the bending stiffness modulus and in the stiffness of the foundation. Uncertainties are represented by parameterized stochastic processes. The random behavior of beam response is modeled using the Askey-Wiener scheme. One contribution of the paper is a sketch of proof of existence and uniqueness of the solution to problems involving fourth order operators applied to random fields. From the approximate Galerkin solution, expected value and variance of beam displacement responses are derived, and compared with corresponding estimates obtained via Monte Carlo simulation. Results show very fast convergence and excellent accuracies in comparison to Monte Carlo simulation. The Askey-Wiener Galerkin scheme presented herein is shown to be a theoretically solid and numerically efficient method for the solution of stochastic problems in engineering.

Improved finite element for 3D laminate frame analysis including warping for any cross-section

The most ordinary finite element formulations for 3D frame analysis do not consider the warping of cross-sections as part of their kinematics. So the stiffness, regarding torsion, should be directly introduced by the user into the computational software and the bar is treated as it is working under no warping hypothesis. This approach does not give good results for general structural elements applied in engineering. Both displacement and stress calculation reveal sensible deficiencies for both linear and non-linear applications. For linear analysis, displacements can be corrected by assuming a stiffness that results in acceptable global displacements of the analyzed structure. However, the stress calculation will be far from reality. For nonlinear analysis the deficiencies are even worse. In the past forty years, some special structural matrix analysis and finite element formulations have been proposed in literature to include warping and the bending-torsion effects for 3D general frame analysis considering both linear and non-linear situations. In this work, using a kinematics improvement technique, the degree of freedom ""warping intensity"" is introduced following a new approach for 3D frame elements. This degree of freedom is associated with the warping basic mode, a geometric characteristic of the cross-section, It does not have a direct relation with the rate of twist rotation along the longitudinal axis, as in existent formulations. Moreover, a linear strain variation mode is provided for the geometric non-linear approach, for which complete 3D constitutive relation (Saint-Venant Kirchhoff) is adopted. The proposed technique allows the consideration of inhomogeneous cross-sections with any geometry. Various examples are shown to demonstrate the accuracy and applicability of the proposed formulation. (C) 2009 Elsevier Inc. All rights reserved.

A BEM model applied to failure analysis of multi-fractured structures

Due to manufacturing or damage process, brittle materials present a large number of micro-cracks which are randomly distributed. The lifetime of these materials is governed by crack propagation under the applied mechanical and thermal loadings. In order to deal with these kinds of materials, the present work develops a boundary element method (BEM) model allowing for the analysis of multiple random crack propagation in plane structures. The adopted formulation is based on the dual BEM, for which singular and hyper-singular integral equations are used. An iterative scheme to predict the crack growth path and crack length increment is proposed. This scheme enables us to simulate the localization and coalescence phenomena, which are the main contribution of this paper. Considering the fracture mechanics approach, the displacement correlation technique is applied to evaluate the stress intensity factors. The propagation angle and the equivalent stress intensity factor are calculated using the theory of maximum circumferential stress. Examples of multi-fractured domains, loaded up to rupture, are considered to illustrate the applicability of the proposed method. (C) 2011 Elsevier Ltd. All rights reserved.

BEM formulation for von Karman plates

This work deals with nonlinear geometric plates in the context of von Karman`s theory. The formulation is written such that only the boundary in-plane displacement and deflection integral equations for boundary collocations are required. At internal points, only out-of-plane rotation, curvature and in-plane internal force representations are used. Thus, only integral representations of these values are derived. The nonlinear system of equations is derived by approximating all densities in the domain integrals as single values, which therefore reduces the computational effort needed to evaluate the domain value influences. Hyper-singular equations are avoided by approximating the domain values using only internal nodes. The solution is obtained using a Newton scheme for which a consistent tangent operator was derived. (C) 2009 Elsevier Ltd. All rights reserved.

A hybrid-Trefftz formulation for plane elasticity with selective enrichment of the approximations

This work is related to the so-called non-conventional finite element formulations. Essentially, a methodology for the enrichment of the initial approximation which is typical of the meshless methods and based on the clouds concept is introduced in the hybrid-Trefftz formulation for plane elasticity. The formulation presented allows for the approximation and direct enrichment of two independent fields: stresses in the domains and displacements on the boundaries of the elements. Defined by a set of elements and interior boundaries sharing a common node, the cloud notion is employed to select the enrichment support for the approximation fields. The numerical analysis performed reveals an excellent performance of the resulting formulation, characterized by the good approximation ability and a reduced computational effort. Copyright (C) 2009 John Wiley & Sons, Ltd.

Proposal of a test specimen to evaluate the shear strength of vertical interfaces of running bond masonry walls

There is no normalized test to assess the shear strength of vertical interfaces of interconnected masonry walls. The approach used to evaluate this strength is normally indirect and often unreliable. The aim of this study is to propose a new test specimen to eliminate this deficiency. The main features of the proposed specimen are failure caused by shear stress on the vertical interface and a small number of units (blocks). The paper presents a numerical analysis based on the finite element method, with the purpose of showing the theoretical performance of the designed specimen, in terms of its geometry, boundary conditions, and loading scheme, and describes an experimental program using the specimen built with full- and third-scale clay blocks. The main conclusions are that the proposed specimen is easy to build and is appropriate to evaluate the sheaf strength of vertical interfaces of masonry walls.

A layered finite element for reinforced concrete beams with bond-slip effects

The behaviour of reinforced concrete members is affected by the slipping of steel bars inserted in the concrete matrix. A tension-stiffening effect and crack evolution occur from the beginning of slipping; thus, the assessment of those phenomena requires the introduction of a bond-slip interaction model. This work presents a beam-layered model, including the constitutive relationships of materials and their interaction, according to the CEB-FIP Model Code 1990. To eliminate the finite element sub-division procedure, a continuous slip function is imposed into the element domain. The results are continuous descriptions of bond stress in the steel-concrete interface, as well as concrete and steel stresses along the element. (C) 2007 Elsevier Ltd. All rights reserved.

Consolidation of elastic-plastic saturated porous media by the boundary element method

This paper presents a domain boundary element formulation for inelastic saturated porous media with rate-independent behavior for the solid skeleton. The formulation is then applied to elastic-plastic behavior for the solid. Biot`s consolidation theory, extended to include irreversible phenomena is considered and the direct boundary element technique is used for the numerical solution after time discretization by the implicit Euler backward algorithm. The associated nonlinear algebraic problem is solved by the Newton-Raphson procedure whereby the loading/unloading conditions are fully taken into account and the consistent tangent operator defined. Only domain nodes (nodes defined inside the domain) are used to represent all domain values and the corresponding integrals are computed by using an accurate sub-elementation scheme. The developments are illustrated through the Drucker-Prager elastic-plastic model for the solid skeleton and various examples are analyzed with the proposed algorithms. (c) 2008 Elsevier B.V. All rights reserved.

A FEM procedure based on positions and unconstrained vectors applied to non-linear dynamic of 3D frames

This study presents an alternative three-dimensional geometric non-linear frame formulation based on generalized unconstrained vector and positions to solve structures and mechanisms subjected to dynamic loading. The formulation is classified as total Lagrangian with exact kinematics description. The resulting element presents warping and non-constant transverse strain modes, which guarantees locking-free behavior for the adopted three-dimensional constitutive relation, Saint-Venant-Kirchhoff, for instance. The application of generalized vectors is an alternative to the use of finite rotations and rigid triad`s formulae. Spherical and revolute joints are considered and selected dynamic and static examples are presented to demonstrate the accuracy and generality of the proposed technique. (C) 2010 Elsevier B.V. All rights reserved.

Topological instability, average electronegativity difference and glass forming ability of amorphous alloys

In this paper, we report the remarkable agreement of the glass forming ability of binary alloys with a new criterion that combines the topological instability parameter (lambda) and the average electronegativity difference among the elements of an alloy, assuming both exert a synergetic effect. The best glass forming compositions for Zr-Cu and Ti-Ni systems are well predicted by this new approach. Although the new criterion needs further refinement, it is concluded that the proposed approach is a promising and simple tool to guide and reduce the tedious and labour intensive work to find good glass former compositions in metallic systems. (C) 2008 Elsevier Ltd. All rights reserved.

Modeling and Analysis of Piezoelectric Energy Harvesting From Aeroelastic Vibrations Using the Doublet-Lattice Method

Multifunctional structures are pointed out as an important technology for the design of aircraft with volume, mass, and energy source limitations such as unmanned air vehicles (UAVs) and micro air vehicles (MAVs). In addition to its primary function of bearing aerodynamic loads, the wing/spar structure of an UAV or a MAV with embedded piezoceramics can provide an extra electrical energy source based on the concept of vibration energy harvesting to power small and wireless electronic components. Aeroelastic vibrations of a lifting surface can be converted into electricity using piezoelectric transduction. In this paper, frequency-domain piezoaeroelastic modeling and analysis of a canti-levered platelike wing with embedded piezoceramics is presented for energy harvesting. The electromechanical finite-element plate model is based on the thin-plate (Kirchhoff) assumptions while the unsteady aerodynamic model uses the doublet-lattice method. The electromechanical and aerodynamic models are combined to obtain the piezoaeroelastic equations, which are solved using a p-k scheme that accounts for the electromechanical coupling. The evolution of the aerodynamic damping and the frequency of each mode are obtained with changing airflow speed for a given electrical circuit. Expressions for piezoaeroelastically coupled frequency response functions (voltage, current, and electrical power as well the vibratory motion) are also defined by combining flow excitation with harmonic base excitation. Hence, piezoaeroelastic evolution can be investigated in frequency domain for different airflow speeds and electrical boundary conditions. [DOI:10.1115/1.4002785]

An electromechanical finite element model for piezoelectric energy harvester plates

Vibration-based energy harvesting has been investigated by several researchers over the last decade. The goal in this research field is to power small electronic components by converting the waste vibration energy available in their environment into electrical energy. Recent literature shows that piezoelectric transduction has received the most attention for vibration-to-electricity conversion. In practice, cantilevered beams and plates with piezoceramic layers are employed as piezoelectric energy harvesters. The existing piezoelectric energy harvester models are beam-type lumped parameter, approximate distributed parameter and analytical distributed parameter solutions. However, aspect ratios of piezoelectric energy harvesters in several cases are plate-like and predicting the power output to general (symmetric and asymmetric) excitations requires a plate-type formulation which has not been covered in the energy harvesting literature. In this paper. an electromechanically coupled finite element (FE) plate model is presented for predicting the electrical power output of piezoelectric energy harvester plates. Generalized Hamilton`s principle for electroelastic bodies is reviewed and the FE model is derived based on the Kirchhoff plate assumptions as typical piezoelectric energy harvesters are thin structures. Presence of conductive electrodes is taken into account in the FE model. The predictions of the FE model are verified against the analytical solution for a unimorph cantilever and then against the experimental and analytical results of a bimorph cantilever with a tip mass reported in the literature. Finally, an optimization problem is solved where the aluminum wing spar of an unmanned air vehicle (UAV) is modified to obtain a generator spar by embedding piezoceramics for the maximum electrical power without exceeding a prescribed mass addition limit. (C) 2009 Elsevier Ltd. All rights reserved.

Hybrid fault diagnosis scheme implementation for power distribution systems automation

Power distribution automation and control are import-ant tools in the current restructured electricity markets. Unfortunately, due to its stochastic nature, distribution systems faults are hardly avoidable. This paper proposes a novel fault diagnosis scheme for power distribution systems, composed by three different processes: fault detection and classification, fault location, and fault section determination. The fault detection and classification technique is wavelet based. The fault-location technique is impedance based and uses local voltage and current fundamental phasors. The fault section determination method is artificial neural network based and uses the local current and voltage signals to estimate the faulted section. The proposed hybrid scheme was validated through Alternate Transient Program/Electromagentic Transients Program simulations and was implemented as embedded software. It is currently used as a fault diagnosis tool in a Southern Brazilian power distribution company.

One-time signature scheme from syndrome decoding over generic error-correcting codes

We describe a one-time signature scheme based on the hardness of the syndrome decoding problem, and prove it secure in the random oracle model. Our proposal can be instantiated on general linear error correcting codes, rather than restricted families like alternant codes for which a decoding trapdoor is known to exist. (C) 2010 Elsevier Inc. All rights reserved,