On boundary conditions for thermally loaded FG beams

Čanađija

International Journal of Engineering Science

2020

In this paper, the mechanical behavior of multilayered small-scale beams in nonisothermal environment is investigated. Scale phenomena are modeled by means of the mathematically well-posed and experimentally consistent stress-driven integral formulation of elasticity. The present research extends the treatment in [1] confined to elastically homogeneous nano-scopic structures. It is shown that the non-locality leads to a complex coupling between axial and transverse elastic displacements. Such a size-dependent phenomenon makes the solution of the relevant nonlocal thermoelastostatic problem, governed by a system of two ordinary differential equations with ten standard boundary conditions and non-classical constitutive boundary conditions, significantly more involved with respect to treatments in literature. Thus, a novel solution methodology, based on Laplace transforms, is proposed and illustrated by examining simple structural schemes of current

Section: Nonisothermal Multilayered Beam Kinematicsmentioning

confidence: 95%

“…The reader is cautioned that if Young modulus is a function of temperature, then the neutral surface shift is also temperature-dependent [51].…”

Section: Position Of the Neutral Surface And Couplingmentioning

confidence: 99%

Section: Introduction Motivation and Outlinementioning

confidence: 99%

See 1 more Smart Citation

On thermomechanics of multilayered beams

Čanađija

International Journal of Engineering Science

2020

“…Mainly nonlocal influence on the mechanical part of the problem is investigated, but buckling caused by the size effect on heat conduction is also analysed [28]. Another recent contribution [29] points out the difference in original and simplified boundary conditions in vibrational and buckling analyses of FG beams in nonisothermal environments. Original boundary conditions do include the thermal moment at the flexural boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

“…Nevertheless, some results including this shift in local problems do exists. For the present research, nonisothermal model [29] is of interest. But, when the nonlocal procedures are concerned, inclusion of the shift of neutral surface is much less common; for the isothermal strain gradient formulation see [35][36][37][38] and for the integral based [39].…”

Section: Introductionmentioning

confidence: 99%

Nonlocal integral thermoelasticity: A thermodynamic framework for functionally graded beams

Čanađija

2019

Composite Structures

An effective nonlocal integral formulation for functionally graded Bernoulli-Euler beams in nonisothermal environment is developed. Both thermal and mechanical loadings are accounted for. The proposed model, of stress-driven integral type, is shown to be governed by a thermodynamically consistent differential problem with proper constitutive boundary conditions. The new thermoelastic strategy is illustrated by investigating a set of examples. It is demonstrated that in nonisothermal statically indeterminate problems rather complex structural behaviours can appear and that both the shift of the neutral surface and nonlocality have a dominating influence at small-scales.

A consistent variational formulation of Bishop nonlocal rods

Faghidian

Continuum Mech. Thermodyn.

2019

Thick rods are employed in Nanotechnology to build modern electro mechanical systems. Design and optimization of such structures can be carried out by nonlocal continuum mechanics which is computationally convenient when compared to atomistic strategies. Bishop's kinematics is able to describe small-scale thick rods if a proper mathematical model of nonlocal elasticity is formulated to capture size effects. In all papers on the matter, nonlocal contributions are evaluated by replacing Eringen's integral convolution with the consequent (but not equivalent) differential equation governed by Helmholtz's differential Both hardening and softening structural responses are predictable with a suitable tuning of the parameters.