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 solid-like FEM for geometrically non-linear 3D frames

This study presents a solid-like finite element formulation to solve geometric non-linear three-dimensional inhomogeneous frames. To achieve the desired representation, unconstrained vectors are used instead of the classic rigid director triad; as a consequence, the resulting formulation does not use finite rotation schemes. High order curved elements with any cross section are developed using a full three-dimensional constitutive elastic relation. Warping and variable thickness strain modes are introduced to avoid locking. The warping mode is solved numerically in FEM pre-processing computational code, which is coupled to the main program. The extra calculations are relatively small when the number of finite elements. with the same cross section, increases. The warping mode is based on a 2D free torsion (Saint-Venant) problem that considers inhomogeneous material. A scheme that automatically generates shape functions and its derivatives allow the use of any degree of approximation for the developed frame element. General examples are solved to check the objectivity, path independence, locking free behavior, generality and accuracy of the proposed formulation. (C) 2009 Elsevier B.V. All rights reserved.

An alternative multi-region BEM technique for three-dimensional elastic problems

The main objective of this work is to present an alternative boundary element method (BEM) formulation for the static analysis of three-dimensional non-homogeneous isotropic solids. These problems can be solved using the classical boundary element formulation, analyzing each subregion separately and then joining them together by introducing equilibrium and displacements compatibility. Establishing relations between the displacement fundamental solutions of the different domains, the alternative technique proposed in this paper allows analyzing all the domains as one unique solid, not requiring equilibrium or compatibility equations. This formulation also leads to a smaller system of equations when compared to the usual subregion technique, and the results obtained are even more accurate. (C) 2008 Elsevier Ltd. All rights reserved.

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.

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.

A STUDY OF PENALTY FORMULATIONS USED IN THE NUMERICAL APPROXIMATION OF A RADIALLY SYMMETRIC ELASTICITY PROBLEM

We consider a class of two-dimensional problems in classical linear elasticity for which material overlapping occurs in the absence of singularities. Of course, material overlapping is not physically realistic, and one possible way to prevent it uses a constrained minimization theory. In this theory, a minimization problem consists of minimizing the total potential energy of a linear elastic body subject to the constraint that the deformation field must be locally invertible. Here, we use an interior and an exterior penalty formulation of the minimization problem together with both a standard finite element method and classical nonlinear programming techniques to compute the minimizers. We compare both formulations by solving a plane problem numerically in the context of the constrained minimization theory. The problem has a closed-form solution, which is used to validate the numerical results. This solution is regular everywhere, including the boundary. In particular, we show numerical results which indicate that, for a fixed finite element mesh, the sequences of numerical solutions obtained with both the interior and the exterior penalty formulations converge to the same limit function as the penalization is enforced. This limit function yields an approximate deformation field to the plane problem that is locally invertible at all points in the domain. As the mesh is refined, this field converges to the exact solution of the plane problem.

Influence of physical and geometrical parameters on three-dimensional load transfer mechanism at tunnel face

Three-dimensional discretizations used in numerical analyses of tunnel construction normally include excavation step lengths much shorter than tunnel cross-section dimensions. Simulations have usually worked around this problem by using excavation steps that are much larger than the actual physical steps used in a real tunnel excavation. In contrast, the analyses performed in this study were based on finely discretized meshes capable of reproducing the excavation lengths actually used in tunnels, and the results obtained for internal forces are up to 100% greater than those found in other analyses available in the literature. Whereas most reports conclude that internal forces depend on support delay length alone, this study shows that geometric path dependency (reflected by excavation round length) is very strong, even considering linear elasticity. Moreover, many other solutions found in the literature have also neglected the importance of the relative stiffness between the ground mass and support structure, probably owing to the relatively coarse meshes used in these studies. The analyses presented here show that relative stiffness may account for internal force discrepancies in the order of 60%. A dimensionless expression that takes all these parameters into account is presented as a good approximation for the load transfer mechanism at the tunnel face.

Verification of a mixed high-order accurate DNS code for laminar turbulent transition by the method of manufactured solutions

This paper presents results on a verification test of a Direct Numerical Simulation code of mixed high-order of accuracy using the method of manufactured solutions (MMS). This test is based on the formulation of an analytical solution for the Navier-Stokes equations modified by the addition of a source term. The present numerical code was aimed at simulating the temporal evolution of instability waves in a plane Poiseuille flow. The governing equations were solved in a vorticity-velocity formulation for a two-dimensional incompressible flow. The code employed two different numerical schemes. One used mixed high-order compact and non-compact finite-differences from fourth-order to sixth-order of accuracy. The other scheme used spectral methods instead of finite-difference methods for the streamwise direction, which was periodic. In the present test, particular attention was paid to the boundary conditions of the physical problem of interest. Indeed, the verification procedure using MMS can be more demanding than the often used comparison with Linear Stability Theory. That is particularly because in the latter test no attention is paid to the nonlinear terms. For the present verification test, it was possible to manufacture an analytical solution that reproduced some aspects of an instability wave in a nonlinear stage. Although the results of the verification by MMS for this mixed-order numerical scheme had to be interpreted with care, the test was very useful as it gave confidence that the code was free of programming errors. Copyright (C) 2009 John Wiley & Sons, Ltd.

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.

Analysis of two reinforced concrete pile caps with embedded sockets in the presence of a locking beam

The present research studies the behavior of reinforced concrete locking beams supported by two capped piles with the socket embedded; used as connections for pre-cast concrete structures. The effect provoked by locking the beam on the pile-caps when supported by the lateral socket walls was evaluated. Three-dimensional numerical analyses using software based on the finite element method (FEM) were developed considering the nonlinear physical behavior of the material. To evaluate the adopted software, a comparative analysis was made using the numerical and experimented results obtained from other software. In the pile caps studied, a variation in the wall thickness, socket interface, strut angle inclination and action on beam. The results show that the presence of a beam does not significantly change pile cap behavior and that the socket wall is able to effectively transfer the force from the beam to the pile caps. By the tensions on the bars of longitudinal reinforcement, it was possible to obtain the force on the tie and the strut angle inclination before the collapse of models. It was found that the angles present more inclinations than those used in the design, which was made based on a strut-and-tie model. More results are available at http://www.set.eesc.usp.br/pdf/download/2009ME_RodrigoBarros.pdf

Power Factor Calculation by the Finite Element Method

The use of finite element analysis (FEA) to design electrical motors has increased significantly in the past few years due the increasingly better performance of modern computers. Even though the analytical software remains the most used tool, the FEA is widely used to refine the analysis and gives the final design to be prototyped. The power factor, a standard data of motor manufactures data sheet is important because it shows how much reactive power is consumed by the motor. This data becomes important when the motor is connected to network. However, the calculation of power factor is not an easy task. Due to the saturation phenomena the input motor current has a high level of harmonics that cannot be neglected. In this work the FEA is used to evaluate a proposed (not limitative) methodology to estimate the power factor or displacement factor of a small single-phase induction motor. Results of simulations and test are compared.

Efficient Modeling of Thin Wires in a Lossy Medium by Finite Elements Applied to Grounding Systems

A procedure is proposed to accurately model thin wires in lossy media by finite element analysis. It is based on the determination of a suitable element width in the vicinity of the wire, which strongly depends on the wire radius to yield accurate results. The approach is well adapted to the analysis of grounding systems. The numerical results of the application of finite element analysis with the suitably chosen element width are compared with both analytical results and those computed by a commercial package for the analysis of grounding systems, showing very good agreement.

Finite element computational modeling of externally bonded CFRP composites flexural behavior in RC beams

This paper focuses on the flexural behavior of RC beams externally strengthened with Carbon Fiber Reinforced Polymers (CFRP) fabric. A non-linear finite element (FE) analysis strategy is proposed to support the beam flexural behavior experimental analysis. A development system (QUEBRA2D/FEMOOP programs) has been used to accomplish the numerical simulation. Appropriate constitutive models for concrete, rebars, CFRP and bond-slip interfaces have been implemented and adjusted to represent the composite system behavior. Interface and truss finite elements have been implemented (discrete and embedded approaches) for the numerical representation of rebars, interfaces and composites.

On the finite element modeling of fatigue crack growth in pressurized cylindrical shells

A methodology for the computational modeling of the fatigue crack growth in pressurized shell structures, based on the finite element method and concepts of Linear Elastic Fracture Mechanics, is presented. This methodology is based on that developed by Potyondy [Potyondy D, Wawrzynek PA, Ingraffea, AR. Discrete crack growth analysis methodology for through crack in pressurized fuselage structures. Int J Numer Methods Eng 1995;38:1633-1644], which consists of using four stress intensity factors, computed from the modified crack integral method, to predict the fatigue propagation life as well as the crack trajectory, which is computed as part of the numerical simulation. Some issues not presented in the study of Potyondy are investigated herein such as the influence of the crack increment size and the number of nodes per element (4 or 9 nodes) on the simulation results by means of a fatigue crack propagation simulation of a Boeing 737 airplane fuselage. The results of this simulation are compared with experimental results and those obtained by Potyondy [1]. (C) 2008 Elsevier Ltd. All rights reserved.

Finite element analysis of concrete cracking at early age

The study of the early age concrete properties is becoming more important, as the thermal effects and the shrinkage, even in the first hours, could generate cracks, increasing the permeability of the structure and being able to induce problems of durability and functionality in the same ones. The detailed study of the stresses development during the construction process can be decisive to keep low the cracking levels. In this work a computational model, based on the finite element method, was implemented to simulate the early age concrete behavior and, specially, the evaluation of the cracking risk. The finite element analysis encloses the computational modeling of the following phenomena: chemical, thermal, moisture diffusion and mechanical which occur at the first days after the concrete cast. The developed software results were compared with experimental values found in the literature, demonstrating an excellent approach for all the implemented analysis.