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 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.

Analysis of the Coupled Stretching-Bending Problem of Stiffened Plates by a BEM Formulation Based on Reissner's Hypothesis

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 beams taking into account the membrane effects. The formulation is derived by assuming a zoned body where each sub-region defines a beam or a slab and all of them are represented by a chosen reference surface. Equilibrium and compatibility conditions are automatically imposed by the integral equations, which treat this composed structure as a single body. In order to reduce the number of degrees of freedom, the problem values defined on the interfaces are written in terms of their values on the beam axis. Initially are derived separated equations for the bending and stretching problems, but in the final system of equations the two problems are coupled and can not be treated separately. Finally are presented some numerical examples whose analytical results are known to show the accuracy of the proposed model.

Analysis of plate bending by means of high order finite hyperelements

The possibilities and limitations of high order hyperelements in plate bending analysis are discussed. Explicit shape functions for some types of triangular elements are given. These elements are applied to simple cases to assess their computational efficiency.

A boundary element formulation for analysis of elastoplastic plates with geometrical nonlinearity

In this paper a new boundary element method formulation for elastoplastic analysis of plates with geometrical nonlinearities is presented. The von Mises criterion with linear isotropic hardening is considered to evaluate the plastic zone. Large deflections are assumed but within the context of small strain. To derive the boundary integral equations the von Karman`s hypothesis is taken into account. An initial stress field is applied to correct the true stresses according to the adopted criterion. Isoparametric linear elements are used to approximate the boundary unknown values while triangular internal cells with linear shape function are adopted to evaluate the domain value influences. The nonlinear system of equations is solved by using an implicit scheme together with the consistent tangent operator derived along the paper. Numerical examples are presented to demonstrate the accuracy and the validity of the proposed formulation.

A C1 finite element for Kirchhoff plate bending

After a short introduction the possibilities and limitations of polynomial simple elements with C1 continuity are discussed with reference to plate bending analysis. A family of this kind of elements is presented.. These elements are applied to simple cases in order to assess their computational efficiency. Finally some conclusions are shown, and future research is also proposed.

An extended BEM formulation for plates reinforced by rectangular beams

This article presents a BEM formulation developed particularly for analysis of plates reinforced by rectangular beams. This is an extended version of a Previous paper that only took into account bending effects. The problem is now re-formulated to consider bending and membrane force effects. The effects of the reinforcements are taken into account by using a simplified scheme that requires application of ail initial stress field to locally correct the bending and stretching stiffness of the reinforcement regions. The domain integrals due to the presence of the reinforcements are then transformed to the reinforcement/plate interface. To reduce the number of degrees of freedom related to the presence of the reinforcement, the proposed model was simplified to consider only bending and stretching rigidities in the direction of the beams. The complete model can be recovered by applying all six internal force correctors, corresponding to six degrees of freedom per node. Examples are presented to confirm the accuracy of the formulation and to illustrate the level of simplification introduced by this strong reduction in the number of degrees of freedom. (C) 2008 Elsevier Ltd. All rights reserved.

BEM formulation for reinforced plates

This article presents a BEM formulation developed to analyse reinforced plate bending. The reinforcements are formulated using a simplified scheme based on applying an initial moment field adopted to locally correct the stiffness of the reinforcement regions. The domain integrals due to the presence of the reinforcements are then transformed to the reinforcement/plate interface. The increase in system stiffness due to the reinforcements can be taken into account independently for each coefficient. Thus, one can conveniently reduce the number of degrees of freedom required in considering the reinforcement. Only one degree-of-freedom is required at each internal node when taking into account only the flexural stiffness of beams. Examples are presented to confirm the accuracy of the formulation. (C) 2009 Elsevier Ltd. All rights reserved.

Análise de pavimentos de edifícios através de uma formulação do método dos elementos de contorno baseada nas hipóteses de Reissner

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A theoretical and experimental analysis of cold-formed steel shapes subjected to bending - Channel and simple lipped channel

Cold-formed steel shapes have been widely employed in steel construction, where they frequently offer a lower cost solution than do traditional laminated shapes. A classic application of cold-formed steel shapes is purlins in the roof panel of industrial buildings, connected to the roof panel by means of screws. The combined effect of these two elements has been the subject of investigations in some countries. Design criteria were included in the AISI Code in 1991 and 1996. This paper presents and discusses the results obtained from bending tests carried out on shapes commonly used in Brazil, i.e., the channel and the simple lipped channel, Tests were carried out on double shapes with 4.5 and 6.0 meter spans, which were subjected to concentrated loads and braced against each other on the supports and at intermediary points in three different load situations. The panel shape was also analyzed experimentally, simulating the action of wind by means of a vacuum box designed specifically for this purpose. The test results were then compared to those obtained through the theoretical analysis, enabling us to extract important information upon which to base proposed design criteria for the new Brazilian code.

Distortional buckling of simple lipped channel in bending results of the experimental analysis versus direct strength methods

Cold-formed steel members are subject to failure caused by buckling, normally under loads smaller than those corresponding to partial or total yielding of the cross section. The buckling of members in bending can be classified as local or global, and the occurrence of one or the other type is expected by the members' geometric characteristics and by the constraints and load conditions. One of the local instability modes that can characterize a member's failure is distortional buckling of the cross section occurring on its own plane and involving lateral displacements and rotations. This paper presents and discusses the procedures and results obtained from experimental tests of cold-formed steel members under bending. Forty-eight beams were carried out on members in simple lipped channel, in pairs, with 6-meter spans and loads applied by concentrated forces at every 1/3 of the span. The thickness, width and dimensions, of the stiffeners were chosen so that the instability by distortion buckling of the cross section was the principal failure mode expected. The experimental results are compared with the obtained results by using the direct strength method.

Analysis of mechanical behavior in bending of polymer composites using the finite elements method

The use of composite materials has increased in the recent decades, mainly in the aeronautics and automotives industries. In the present study is elaborated a computational simulation program of the bending test using the finite elements method, in the commercial software ANSYS. This simulation has the objective of analyze the mechanical behavior in bending of two composites with polymeric matrix reinforced with carbon fibers. Also are realized bending tests of the 3 points to obtain the resistances of the materials. Data from simulation and tests are used to make a comparison between two failures criteria, Tsai-Wu and Hashin criterion. Copyright © 2009 SAE International.

Analysis of the Stresses in Corrugated Sheets under Bending

This paper presents three different numerical models for the evaluation of the stresses in corrugated sheets under bending. Regarding the numerical simulations different approaches can be considered, i.e., a elastic linear analysis or a physical nonlinear analysis, that considers criteria to fail for the sheet material. Moreover, the construction of the finite element mesh can be used shell elements or solid elements. The choice of each finite element must be made from the consideration of their representativity before behavior to be simulated. Thus, the numerical modelling in this manuscript was performed from the three-dimensional models using the SAP2000Nonlinear software, version 7.42, which has as base the finite elements method (FEM). It was considered shell elements in the build the mesh of finite elements and an analysis of type elastic linear in this case. Five mm thick sheets were evaluated considering three different longitudinal dimensions (spans), i.e., 1100 mm, 1530 mm and 1830 mm. The applied load to the models was 2500 N/m and it was verified that the spans of support of sheets have a significant influence on the results of stresses. The sheets with larger spans present larger stresses for the same applied load. The most intense values of tension occur in the troughs (low waves) of the sheets, on the lower surface, while the most intense values of compression occur in the crests (high waves), on the upper surface of the sheet. The flanks, which are the parts among the troughs and crests of the sheets, are submitted to low levels of stresses. The numeric results of the stresses showed a good agreement with the results obtained from other researchers(3) and these results can be used to predict the behavior of corrugated sheets under bending.

A computer program for the analysis of the dynamic bending-torsion coupling in bridges using a mini-computer

The analysis of modes and natural frequencies is of primary interest in the computation of the response of bridges. In this article the transfer matrix method is applied to this problem to provide a computer code to calculate the natural frequencies and modes of bridge-like structures. The Fortran computer code is suitable for running on small computers and results are presented for a railway bridge.

A comparative analysis between FEM and Boundary Methods in bending of Plates

Two different methods of analysis of plate bending, FEM and BM are discussed in this paper. The plate behaviour is assumed to be represented by using the linear thin plate theory where the Poisson-Kirchoff assumption holds. The BM based in a weighted mean square error technique produced good results for the problem of plate bending. The computational effort demanded in the BM is smaller than the one needed in a FEM analysis for the same level of accuracy. The general application of the FEM cannot be matched by the BM. Particularly, different types of geometry (plates of arbitrary geometry) need a similar but not identical treatment in the BM. However, this loss of generality is counterbalanced by the computational efficiency gained in the BM in the solution achievement