Static bending analysis of two-directional functionally graded beam using simple Timoshenko beam elements

This article presents the static bending of two-directional functionally graded (FG) beam by using simple Timoshenko beam elements. The Matlab code developed based on the finite element formulation is validated by solving two-directional FG beam problems under distributed load and two boundary conditions. Numerical results which are in terms of maximum normalized transverse deflections are compared with the analytical solutions and the results from previous studies. Besides, the shapes of transverse deflection and rotation along the length of beams are also depicted in this article to provide specific views about the static behavior of proposed structure

A Notion in Modeling Concrete Members

In this paper, the influence of aggregate size on width of fracture process zone wc is considered. Some researchers observed that the greater the grains of aggregate, the wider the fracture process zone (FPZ). The average value of the FPZ width taken from tests performed by Woliński was 26.6 mm and it did not depend on maximum aggregate size Dmax. There are no consistent conclusions as to whether the width of FPZ depends on aggregate size, and there are no standard methods of FPZ width measurement. The problem arises how to choose the width of FPZ in numerical modeling of concrete structures. For example, Bažant and Oh proposed to take wc = 3Dmax in numerical calculations. To discuss this problem, the authors’ own numerical simulations concerning bent concrete members with different widths of FPZ: 5, 10, 20, 26.5, 50 and 100 mm were performed. On the basis of the comparison of obtained results, significant differences dependent on wc have been observed. Taking into account the minimum potential energy in a member, it can be said that the most rational thing to do is to take the smallest elongation within the localized microcracking. This condition takes place in the analyzed beam when wc = 50 mm. The assumption wc = 3Dmax does not fit this criterion. Also, the width from the experiment performed by Woliński is not in good relation to obtained numerical results. The main conclusion from this paper is that the width of FPZ does have an influence on obtained numerical results performed by crack band model. The problem of estimating the width of FPZ in numerical simulations exists and requires further research

Static bending analysis of two-directional functionally graded beam using simple Timoshenko beam elements

This article presents the static bending of two-directional functionally graded (FG) beam by using simple Timoshenko beam elements. The Matlab code developed based on the finite element formulation is validated by solving two-directional FG beam problems under distributed load and two boundary conditions. Numerical results which are in terms of maximum normalized transverse deflections are compared with the analytical solutions and the results from previous studies. Besides, the shapes of transverse deflection and rotation along the length of beams are also depicted in this article to provide specific views about the static behavior of proposed structure

A study of functionally graded porous beam based on simple beam theory

In this article, the bending behaviors of functionally graded porous (FGP) beams are determined associated with uniform load. The simple beam theory is carried out with various boundary conditions. Two types of porosity are also applied to study the influences of material properties on bending behaviors. The results obtained in this article are presented and compared with other results in the references to verify the correctness in implementing the formula and writing the Matlab code. Last but not least, this article can help researchers to have an overview of the bending characteristics of the functionally graded porous beams

A study of functionally graded porous beam based on simple beam theory

In this article, the bending behaviors of functionally graded porous (FGP) beams are determined associated with uniform load. The simple beam theory is carried out with various boundary conditions. Two types of porosity are also applied to study the influences of material properties on bending behaviors. The results obtained in this article are presented and compared with other results in the references to verify the correctness in implementing the formula and writing the Matlab code. Last but not least, this article can help researchers to have an overview of the bending characteristics of the functionally graded porous beams