Márcio Eduardo Silveira

Emprego de ferramentas numéricas na avaliação do módulo de elasticidade em vigas roliças de madeira

Beams are structural elements used in the most of civil constructions. The wood can be found in several applications of engineering due to the moderate mechanical strength and low density. The use of round timber as a beam is very attractive, since it does not need to be processed, such as lumber. The design of structural timber elements requires the determination of its physical and mechanical properties in which are obtained based on the recommendations of engineering standards. In case of round timber, the national standards dealing with the determination of strength and stiffness properties are in term for more than twenty years with no technical review. Overall, both national and international standards consider truncated-cone geometry for cylindrical logs of wood, resulting in simplified equations unable to predict the effect of shape irregularities on the longitudinal modulus of elasticity. This paper aims to evaluate the effect of shape irregularity of round timber of Corymbia citriodora and Pinus caribaea to determine the longitudinal modulus of elasticity. The three-point bending test is used to determine the modulus, considering a simplified analytical model, with constant circular section for the element. The irregularities of the wood are considered in the numerical models based on a beam and three-dimensional finite elements. The results showed statistical equivalence between the modulus of elasticity for both methods of calculation, indicating that the constant circular section is a reasonable assumption for the wooden here evaluated.

Numerical Analyses of Timber Columns Reinforced by Particulate Composite Material

Beams are structural elements commonly used in structure for construction designs. Usually wood is applied as structural elements and its use is very important because it is a material of renewable source, low density and satisfactory mechanical performance. When the wood surface is not properly treated, the structure can be destroyed not only by environmental conditions but also the attack of insects, compromising the structural design. This research presents the use of a particulate composite material of epoxy resin reinforced with white Portland cement in order to be applied as repair in timber columns. The mechanical performance of this material is essentially numerical, based on the Finite Element Method. The wood used in the simulation was the Eucalyptus grandis. The elastic properties were obtained from the specialist literature in the field of timber structures. The results of numerical simulations in terms of tension and buckling loads, the inclusion of the composite in the damaged regions (for all dimensions of the defects studied) provided buckling load results significantly higher than the buckling load values for the conditions without composite, and near to the values of the buckling loads without defect, highlighting the good performance of the particulate composite material in the repair of timber columns. INTRODUCTION Columns and beams are fundamental elements in the majority of structures. In a building, we highlight the use of wood for being a renewable source material, presenting excellent relationship between strength and density, according to [1] this gets to be four times higher when compared to steel. The wood, which until the early twentieth century represented one of the main structural materials in construction [2]. The buildings constructed with wood require appropriate maintenance and use. According to [3], structural elements of wood are susceptible to variations in their mechanical properties due to natural factors, such as growing conditions Accepted: November 5, 2015 * Address correspondence to this author at the Centre for Innovation and Technology in Composites (CITeC), Department of Civil Engineering (DECiv), Federal University of São Carlos (UFSCar), São Carlos, 13565-905, Brazil; Tel: (+55) 16 33066828; E-mail: christoforoal@yahoo.com.br

AVALIAÇÃO NUMÉRICA DO MÓDULO DE ELASTICIDADE EM VIGAS ROLIÇAS DE MADEIRA DA ESPÉCIE Pinus elliottii

This research aimed to present a numerical methodology of calculation, based on the Finite Element Method and the Least Squares Method, to determine de longitudinal modulus of elasticity in structural round timber beams, considering the irregularities in the geometry of the elements by linear approximation along the finite elements. In addition with the numerical model (1D), together, two others were used, one analytical (1D simplified), which considers a single value of diameter (cylindrical geometry), measured at the midpoint of the elements, and another numerical model (3D), allows more accurately to delineate the geometry of the element, enabling check the difference between them. Therefore, the beams were evaluated according to the static three-point bending test, being tested twenty four elements of Pinus elliottii wood species, with average length of 630 cm, breast height diameter around 21 cm, green wood (satured), tape average of 6% and mean of factor form section of 0,82. The results of the confidence interval between the modulus of elasticity of the 1D numerical model (E o ) and analytical (E deq ) showed statistical equivalence between the methodologies, justified by the small taper of the elements, may be different for others tapers. The use of the longitudinal modulus of elasticity obtained from de numerical 1D model in the 3D simulations of the round timber beams lead to displacement values equivalent to those obtained in the tests, proving the efficiency of 1D numerical model, requiring less computational work.

O USO DE OTIMIZAÇÃO NUMÉRICA NO PROJETO DE BLANKS SOLDADOS

A otimizacao topologica e frequentemente referenciada na literatura como otimizacao de forma generalizada (ou otimizacao de layout). A importância deste tipo de otimizacao encontra-se no fato de que, a escolha de uma topologia apropriada de um componente, na etapa conceitual, e geralmente, um dos fatores mais decisivos para a eficiencia de um novo produto. A utilizacao de blanks soldados na industria automotiva tem permitido otimizar o projeto de um determinado componente, pois e possivel unir acos de diferentes espessuras, graus de conformabilidade e resistencia mecânica em um unico blank, que apos a sua estampagem, pode ter seu desempenho otimizado pela configuracao adequada dos acos que o compoem. A definicao do arranjo de um blank soldado depende tanto dos esforcos que a peca final tera em uso como tambem das deformacoes sofridas durante seu processo de conformacao. Este trabalho consisti em usar tecnicas de otimizacao topologica e simulacao de estampagem via Aproximacao Inversa para estimar o arranjo inicial de um blank soldado tendo como restricao a Curva Limite de Conformacao dos materiais. Em uma segunda etapa, a otimizacao topologica com restricao em massa foi utilizada para maximizar a rigidez do componente em uso. Palavras-chave: Blank soldado, Aproximacao Inversa, Otimizacao Topologica. ABSTRACT Topology optimization is often referenced in literature as a layout optimization (or a generalized shape optimization). The importance of this type of optimization is the fact that the choice of an appropriate topology for a component, in conceptual stage is generally one of the most decisive factors for the efficiency of a new product. The use of tailor welded blanks in the automotive industry has allowed to optimize the design of a given component, because it is possible to combine steels with different thickness, degree of formability and mechanical strength in a single blank, which after the stamping, can be its performance optimized by proper configuration of the steel. The layout design of a tailor welded blanks depends on both the efforts that the final component will have in use as well as the strain during its forming process. This work consisted in use of topology optimization techniques and simulation of stamping via Inverse Approach to estimate the initial layout of a tailor welded blank, with constraint on Forming Limit Curve. In a second step, the topology optimization with mass constraint was used to maximize the stiffness of the component in use. Keywords: Tailor Welded Blank, Inverse Approach, Topology Optimization.