BEM Formulations Based on Kirchhoff's Hypoyhesis to Perform Linear Bending Analysis of Plates Reinforced by Beams

In this work, are discussed two formulations of the boundary element method - BEM to perform linear bending analysis of plates reinforced by beams. Both formulations are based on the Kirchhoffs hypothesis and they are obtained from the reciprocity theorem applied to zoned plates, where each sub-region defines a beam or a stab. In the first model the problem values are defined along the interfaces and the external boundary. Then, in order to reduce the number of degrees of freedom kinematics hypothesis are assumed along the beam cross section, leading to a second formulation where the collocation points are defined along the beam skeleton, instead of being placed on interfaces. on these formulations no approximation of the generalized forces along the interface is required. Moreover, compatibility and equilibrium conditions along the interface are automatically imposed by the integral equation. Thus, these formulations require less approximation and the total number of the degrees of freedom is reduced. In the numerical examples are discussed the differences between these two BEM formulations, comparing as well the results to a well-known finite element code.

A BEM formulation for analysing the coupled stretching-bending problem of plates reinforced by rectangular beams with columns defined in the domain

In this work, a boundary element formulation to analyse plates reinforced by rectangular beams, with columns defined in the domain is proposed. The model is based on Kirchhoff hypothesis and the beams are not required to be displayed over the plate surface, therefore eccentricity effects are taken into account. The presented boundary element method formulation is derived by applying the reciprocity theorem to zoned plates, where beams are treated as thin sub-regions with larger rigidities. The integral representations derived for this complex structural element consider the bending and stretching effects of both structural elements working together. The standard equilibrium and compatibility conditions along interface are naturally imposed, being the bending tractions eliminated along interfaces. The in-plane tractions and the bending and in-plane displacements are approximated along the beam width, reducing the number of degrees of freedom. The columns are introduced into the formulation by considering domain points where tractions can be prescribed. Some examples are then shown to illustrate the accuracy of the formulation, comparing the obtained results with other numerical solutions.

NUMERICAL SIMULATION of THE BEHAVIOR of THE BEHAVIOR of REINFORCED CONCRETE BEAMS and COLUMNS BY FEM CAASTEM 2000 PROGRAM

The objective of this paper is the numerical study of the behavior of reinforced concrete beams and columns by non-linear numerical simulations. The numerical analysis is based on the finite element method implemented in CASTEM 2000. This program uses the constitutive elastoplastic perfect model for the steel, the Drucker-Prager model for the concrete and the Newton-Raphson for the solution of non-linear systems. This work concentrates on the determination of equilibrium curves to the beams and force-strain curves to the columns. The numeric responses are confronted with experimental results found in the literature in order to check there liability of the numerical analyses.

Cortical Bone Stress Distribution in Mandibles with Different Configurations Restored with Prefabricated Bar-Prosthesis Protocol: A Three-Dimensional Finite-Element Analysis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Fracture resistance of endodontically treated teeth with different heights of crown ferrule restored with prefabricated carbon fiber post and composite resin core by intermittent loading

This study evaluated the fracture resistance of endodontically treated teeth restored with prefabricated carbon fiber posts and varying quantities of coronal dentin. Sixty freshly extracted upper canines were randomly divided into groups of 10 teeth each. The specimens were exposed to 250,000 cycles in a controlled chewing simulator. All intact specimens were subjected to a static load (N) in a universal testing machine at 45 degrees to the long axis. Data were analyzed by 1-way analysis of variance and Tukey test (alpha = .05). Significant differences (P < .001) were found among the mean fracture forces of the test groups (positive control, 0 mm, 1 mm, 2 mm, 3 mm, and negative control groups: 1022.82 N, 1008.22 N, 1292.52 N, 1289.19 N, 1255.38 N, and 1582.11, respectively). These results suggested that the amount of coronal dentin did not significantly increase the fracture resistance of endodontically treated teeth restored with prefabricated carbon fiber post and composite resin core. (Oral Surg Oral Med Oral Pathol Oral Radiol Endod 2008;106:e52-e57)

Remarks on Bessel beams, signals and superluminality

We address the question about the velocity of signals carried by Bessel beams wave packets propagating in vacuum and having well defined wavefronts in time. We find that this problem in analogous to that of propagation of usual plane wave packets within dispersive media and conclude that the signal velocity cannot be superluminal. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Study of stress distribution with finite element method in a root with prefabricated threaded split shaft post - Part I

A finite element analysis was carried out to study the role of prefabricated threaded split shaft post (Flexi-Post) on dentinal stress in pulpless tooth. Three dimensional plane strain model of mesio-distal section of a human maxillary central incisor without restoration was analysed with the MSC/NASTRAN (MacNeal/ Schwendler) general purpose finite analysis program was executed on a microcomputer. The model as discretized into 48.954 axisymmetric finite elements defined by 10.355 nodes. Each element was assigned unique elastic properties to represent the materials modeled. Homogeneity, isotropy and linear elasticity were assume for all material. A simulation of static load of 100N was applied to the incisal edge of the post; vertical. Maximal principal stresses and von Mises equivalent stress were calculated. Using the element analysis model employed in this study, the following can be concluded concerning threaded split shaft post (Flexi-Post): Maximum principal stresses in dentin were located at cervical place and at the post apex. The apical threads of the post not redirecting stresses away from the root.

Non-linear boundary element analysis of floor slabs reinforced with rectangular beams

In this work, a numerical model to perform non-linear analysis of building floor structures is proposed. The presented model is derived from the Kirchhoff-s plate bending formulation of the boundary element method (BENI) for zoned domains, in which the plate stiffness is modified by the presence of membrane effects. In this model, no approximation of the generalized forces along the interface is required and the compatibility and equilibrium conditions along interfaces are imposed at the integral equation level. In order to reduce the number of degrees of freedom, the Navier Bernoulli hypothesis is assumed to simplify the strain field for the thin sub-regions (rectangular beams). The non-linear formulation is obtained from the linear formulation by incorporating initial internal force fields, which are approximated by using the well-known cell sub-division. Then, the non-linear solution of algebraic equations is obtained by using the concept of the consistent tangent operator. The Von Mises criterion is adopted to govern the elasto-plastic material behaviour checked at points along the plate thickness and along the rectangular beam element axes. The numerical representations are accurately obtained by either computing analytically the element integrals or performing the numerical integration accurately using an appropriate sub-elementation scheme. (C) 2007 Elsevier Ltd. All rights reserved.

Numeric evaluation of the stiffness of log-concrete composite beams submitted the cyclical load

In this paper was evaluated, using the software ANSYS, the stiffness (El) of the log-concrete composite beams, of section T, with connectors formed by bonded-in steel rods, type CA-50, disposed in X, with application of cyclical load. The stiffness of the system was evaluated through the simulation of bending tests, considered 1/2 beam, with cyclical shipment varying among 40 % and 5 % of the strength of the connection with the load relationship R=0,125, for a total of 10 load cycles applied. The numeric results show a good agreement with experimental tests.

A BEM formulation based on Reissner's theory to perform simple bending analysis of plates reinforced by rectangular beams

In this work, the plate bending formulation of the boundary element method (BEM), based on the Reissner's hypothesis, is extended to the analysis of plates reinforced by rectangular beams. This composed structure is modelled by a zoned plate, being the beams represented by narrow sub-regions with larger thickness. The integral equations are derived by applying the weighted residual method to each sub-region, and summing them to get the equation for the whole plate. Equilibrium and compatibility conditions are automatically imposed by the integral equations, which treat this composed structure as a single body. In order to decrease the number of degrees of freedom, some approximations are considered for both displacements and tractions along the beam width. The accuracy of the proposed model is illustrated by simple examples whose exact solution are known as well as by more complex examples whose numerical results are compared with a well-known finite element code.

Niobium filtration of conventional and high-frequency x-ray generator beams for intraoral radiography. Effects on absorbed doses, image density and contrast, and photon spectra

We have studied the effects of niobium beam filtration on absorbed doses, on image density and contrast, and on photon spectra with conventional and high-frequency dental x-ray generators. Added niobium reduced entry and superficial absorbed doses in periapical radiography by 9% to 40% with film and digital image receptors, decreased the radiation necessary to produce a given image density on E-speed film and reduced image contrast on D- and E-speed films. As shown by increased half-value layers for aluminum, titanium, and copper and by pulse-height analyses of beam spectra, niobium increased average beam energy by 6% to 19%. Despite the benefits of adding niobium on patient dose reduction and on narrowing the beams' energy spectra, the beam can be overhardened. Adding niobium, therefore, strikes the best balance between radiation dose reduction and beam attenuation, with its risks of increased exposure times, motion blur, and diminished image contrast, when it is used at modest thicknesses (30 μm) and at lower kVp (70) settings. © 1995 Mosby-Year Book, Inc.

A contribution for nonlinear structural dynamics characterization of cantilever beams

Successful experiments in nonlinear vibrations have been carried out with cantilever beams under harmonic base excitation. A flexible slender cantilever has been chosen as a convenient structure to exhibit modal interactions, subharmonic, superharmonic and chaotic motions, and others interesting nonlinear phenomena. The tools employed to analyze the dynamics of the beam generally include frequency- and force-response curves. To produce force-response curves, one keeps the excitation frequency constant and slowly varies the excitation amplitude, on the other hand, to produce frequency-response curves, one keeps the excitation amplitude fixed and slowly varies the excitation frequency. However, keeping the excitation amplitude constant while varying the excitation frequency is a difficult task with an open-loop measurement system. In this paper, it is proposed a closed-loop monitor vibration system available with the electromagnetic shaker in order to keep the harmonic base excitation amplitude constant. This experimental setup constitutes a significant improvement to produce frequency-response curves and the advantages of this setup are evaluated in a case study. The beam is excited with a periodic base motion transverse to the axis of the beam near the third natural frequency. Modal interactions and two-period quasi-periodic motion are observed involving the first and the third modes. Frequency-response curves, phase space and Poincaré map are used to characterize the dynamics of the beam.

Fiberglass-reinforced glulam beams: Mechanical properties and theoretical model

The glued-laminated lumber (glulam) technique is an efficient process for making rational use of wood. Fiber-Reinforced Polymers (FRPs) associated with glulam beams provide significant gains in terms of strength and stiffness, and also alter the mode of rupture of these structural elements. In this context, this paper presents a theoretical model for designing reinforced glulam beams. The model allows for the calculation of the bending moment, the hypothetical distribution of linear strains along the height of the beam, and considers the wood has a linear elastic fragile behavior in tension parallel to the fibers and bilinear in compression parallel to the fibers, initially elastic and subsequently inelastic, with a negative decline in the stress-strain diagram. The stiffness was calculated by the transformed section method. Twelve non-reinforced and fiberglass reinforced glulam beams were evaluated experimentally to validate the proposed theoretical model. The results obtained indicate good congruence between the experimental and theoretical values.

Reliability of timber bridges using nailed plywood box beams

The Nailed Box Beam structural efficiency is directly dependent of the flange-web joint behavior, which determines the partial composition of the section, as the displacement between elements reduces the effective rigidity of the section and changes the stress distribution and the total displacement of the section. This work discusses the use of Nailed Plywood Box Beams in small span timber bridges, focusing on the reliability of the beam element. It is presented the results of tests carried out in 21 full scale Nailed Plywood Box Beams. The analysis of maximum load tests results shows that it presents a normal distribution, permitting the characteristic values calculation as the normal distribution theory specifies. The reliability of those elements was analyzed focusing on a timber bridge design, to estimate the failure probability in function of the load level.