‎let $x$ be a real normed  space, then  $c(subseteq x)$  is  functionally  convex  (briefly, $f$-convex), if  $t(c)subseteq bbb r $ is  convex for all bounded linear transformations $tin b(x,r)$; and $k(subseteq x)$  is  functionally   closed (briefly, $f$-closed), if  $t(k)subseteq bbb r $ is  closed  for all bounded linear transformations $tin b(x,r)$. we improve the    krein-milman theorem  ...

in this paper, the influence of the constituent volume fractions by changing the values of the power-law exponent with uniform pressure on the vibration frequencies of reinforced functionally graded cylindrical shells is studied. the fgm shell with ring is developed in accordance to the volume fraction law from two constituents namely stainless steel and nickel. these constituents are graded th...

this paper deals with the determination of displacement function and thermal stresses of a finite length isotropic functionally graded hollow cylinder subjected to uniform temperature field. the solution of the governing thermoelastic equation is obtained, as suggested by spencer et al. for anisotropic laminates.  numerical calculations are also carried out for fgm (functionally graded material...

this paper deals with local buckling analysis of rectangular functionally graded material plates using finite strip method and based on classical plate theory. the modulus of elasticity of the plate is assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents. the principle of minimum total potential energy is employed to obtain stiffness and sta...

In this paper, the modified couple stress theory is used to study vibration analysis of functionally graded rectangular micro-plates. Considering classical and first order plate theories, the couple governing equations of motion are obtained by using the Hamilton’s principle. Considering an assumed mode method, the accurate size dependent natural frequencies are established for simply supported...

Safety analysis has been done for the torsion of a functionally graded thick-walled  circular cylinder under internal and external pressure subjected to thermal loading. In order to determine stresses the concept of Seth’s transition theory based on generalized principal strain measure has been used. This theory simplifies the set of mechanical equations by mentioning the order of the measure of...

the current study presents a new analytical method for buckling analysis of rectangular and annular beams made up of functionally graded materials with constant thickness and poisson’s ratio. the boundary conditions of the beam are assumed to be simply supported and clamped. the stability equations were obtained by using conservation of energy. the critical buckling load and first mode shape we...

the current study presents a new analytical method for buckling analysis of circular plates with constant thickness and poisson’s ratio, made of functionally graded material subjected to radial load. governing equations are based on energy method for thin plates. the boundary conditions of the plate are assumed to be simply supported and clamped. the stability equations were obtained by using c...

functionally gradedpoisson’s ratio structures have been developed for critical protection. in thispaper, the static bending and buckling of fgpr nanoscale beam are studied basedon the nonlocal timoshenko beam model, in which both young’s modulus andpoisson’s ratio are assumed to vary continuously in the thickness direction. byutilizing total potential energy principle, equilibrium equations are...