Static Analysis of FG Beams via Complementary Functions Method

Abstract

The bending response of Functionally Graded (FG) beams is carried out by the Complementary Functions Method (CFM). The mechanical properties of the material, Young's modulus, of the straight beams are considered to be graded only in the thickness direction. Poisson's ratio is supposed to be constant. Governing equations of the considered problem are obtained with the aid of minimum total potential energy principle based on Timoshenko's beam theory (FSDT). The main purpose of this paper is the infusion of the CFM to the bending analysis of FG straight beams. The effectiveness and accuracy of the proposed scheme are confirmed by comparing its numerical results with those of the available literature. The application of this efficient method provides accurate results of static response for FGM beams with different variations of material properties.

Analysis of Elastic Lateral Torsional Buckling of Cantilever I Sections by the Complementary Functions Method

“…In this equation q stands for the magnitude of uniformly distributed load. The variables given in equations (3-6) will be used to convert equation (11) to a set of ordinary canonical differential equations.…”

“…The set of canonical equations obtained from equations (2), equations (11), equations (16) and equations ( 21) are two-point boundary value problems. The CFM will be implemented to carry out the solution of these equations.…”

“…The main principle is the implemented method is that it reduces a two-point boundary value problem to an initial value problem. The solution of the set of the ordinary differential equations can be given in equation ( 26) which is consist of four homogenous and one nonhomogeneous solution [10,11]. In the solution procedure of the initial value problem the Runge -Kutta (5 th order) will be used [12].…”

Winkler Tipi Elastik Zemine Oturan Fonksiyonel Derecelenmiş Malzemeli Kirişlerin Statik Analizi

“…Zghal ve arkadaşları, kalınlık yönünde FD boşluklu kirişlerin statik eğilme davranışını karışık sonlu elemanlar yöntemi ile araştırmıştır [19]. Literatürde çeşitli mühendislik mekaniği problemleri TFY kullanarak araştırılmıştır [20][21][22][23][24][25][26].…”

Finite Element Analysis for the Static Response of Functionally Graded Porous Sandwich Beams

“…The displacement aspect established on higher-order shear deformation theory is applied by [20] to study the static behavior of functionally graded metal-ceramic functionally graded material beams under surrounded temperature. By the method of complementary functions, the bending of functionally graded beams is defined by [21]. Depending on the theory of Bernoulli, and Timoshenko the equations governing the bending response of sandwich beams were obtained by [22].…”