purpose– analysis of non-prismatic beams has been focused of attention due to wide use in complex structures such as aircraft, turbine blades and space vehicles. apart from aesthetic aspect, optimization of strength and weight is achieved in use of this type of structures. the purpose of this paper is to present new shape functions, namely 3-node basic displacement functions (bdfs) for derivati...

the accuracy and efficiency of the elements proposed by finite element method (fem) considerably depend on the interpolating functions namely shape functions used to formulate the displacement field within the element. in the present study, novel functions, namely basic displacements functions (bdfs), are introduced and exploited for structural analysis of nanobeams using finite element method ...

Purpose– Analysis of non-prismatic beams has been focused of attention due to wide use in complex structures such as aircraft, turbine blades and space vehicles. Apart from aesthetic aspect, optimization of strength and weight is achieved in use of this type of structures. The purpose of this paper is to present new shape functions, namely 3-node Basic Displacement Functions (BDFs) for derivati...

The accuracy and efficiency of the elements proposed by finite element method (FEM) considerably depend on the interpolating functions namely shape functions used to formulate the displacement field within the element. In the present study, novel functions, namely basic displacements functions (BDFs), are introduced and exploited for structural analysis of nanobeams using finite element method ...

This paper aims at presenting a new efficient element for free vibration and instability analysis of Axially Functionally Graded Materials (FGMs) non-prismatic beams using Finite Element Method (FEM). Using concept of Basic Displacement Functions (BDFs), two- node element extends  to three-node element for obtaining much more exact results using FEM. First, BDFs are introduced and computed usin...

The present paper is aimed to study an exact analysis of the free vibrations of a simply supported, homogeneous, transversely isotropic, cylindrical panel based on three-dimensional generalized theories of thermoelastic diffusion. After applying the displacement potential functions in the basic governing equations of generalized thermoelastic diffusion, it is noticed that a purely transverse mo...

The solution of ordinary differential equations (ODEs) is intrinsically bound up with the solution of partial differential equations (PDEs). In this chapter the basic integration methods are introduced, covering: Euler, Runge-Kutta, variable step, extrapolation, BDFs, NDFs, and Adams. Various test examples for the different integration methods are provided along with annotated code. The Newton ...

In this study, stress and displacement functions of the three-dimensional theory of elasticity for homogeneous isotropic bodies are derived from first principles from the differential equations of equilibrium, the generalized stress – strain laws and the geometric relations of strain and displacement. It is found that the stress and displacement functions must be biharmonic functions. The deriv...