Displaying similar documents to “Nonlocal theory of curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models”

Micropolar curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models

V.V. Zozulya (2017)

Curved and Layered Structures

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New models for micropolar plane curved rods have been developed. 2-D theory is developed from general 2-D equations of linear micropolar elasticity using a special curvilinear system of coordinates related to the middle line of the rod and special hypothesis based on assumptions that take into account the fact that the rod is thin.High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First stress...

Couple stress theory of curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models

V.V. Zozulya (2017)

Curved and Layered Structures

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New models for plane curved rods based on linear couple stress theory of elasticity have been developed.2-D theory is developed from general 2-D equations of linear couple stress elasticity using a special curvilinear system of coordinates related to the middle line of the rod as well as special hypothesis based on assumptions that take into account the fact that the rod is thin. High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series...

Anisotropic viscoelastic body subjected to the pulsating load

Jozef Sumec, Mária Minárová, Ľuboš Hruštinec (2023)

Applications of Mathematics

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Constitutive equations of continuum mechanics of the solid phase of anisotropic material is focused in the paper. First, a synoptic one-dimensional Maxwell model is explored, subjected to arbitrary deformation load. The explicit form is derived for stress on strain dependence. Further, the analogous explicit constitutive equation is taken in three spatial dimensions and treated mathematically. Later on, a simply supported straight concrete beam reinforced by the steel fibres is taken...

A hybrid procedure to identify the optimal stiffness coefficients of elastically restrained beams

Tiago Silva, Maria Loja, Nuno Maia, Joaquim Barbosa (2015)

International Journal of Applied Mathematics and Computer Science

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The formulation of a bending vibration problem of an elastically restrained Bernoulli-Euler beam carrying a finite number of concentrated elements along its length is presented. In this study, the authors exploit the application of the differential evolution optimization technique to identify the torsional stiffness properties of the elastic supports of a Bernoulli-Euler beam. This hybrid strategy allows the determination of the natural frequencies and mode shapes of continuous beams,...

Bending analysis of laminated composite and sandwich beams according to refined trigonometric beam theory

A. S. Sayyad, Y. M. Ghugal, N. S. Naik (2015)

Curved and Layered Structures

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A trigonometric beam theory (TBT) is developed for the bending analysis of laminated composite and sandwich beams considering the effect of transverse shear deformation. The axial displacement field uses trigonometric function in terms of thickness coordinate to include the effect of transverse shear deformation. The transverse displacement is considered as a sum of two partial displacements, the displacement due to bending and the displacement due to transverse shearing. Governing equations...

Analysis of Smart Piezo-Magneto-Thermo-Elastic Composite and Reinforced Plates: Part II – Applications

D. A. Hadjiloizi, A.L. Kalamkarov, Ch. Metti, A. V. Georgiades (2014)

Curved and Layered Structures

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A comprehensive micromechanical model for the analysis of a smart composite piezo-magneto-thermoelastic thin plate with rapidly varying thickness is developed in Part I of thiswork. The asymptotichomogenization model is developed using static equilibrium equations and the quasi-static approximation of Maxwell’s equations. The work culminates in the derivation of general expressions for effective elastic, piezoelectric, piezomagnetic, dielectric permittivity and other coefficients. Among...

On implicit constitutive theories

Kumbakonam R. Rajagopal (2003)

Applications of Mathematics

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In classical constitutive models such as the Navier-Stokes fluid model, and the Hookean or neo-Hookean solid models, the stress is given explicitly in terms of kinematical quantities. Models for viscoelastic and inelastic responses on the other hand are usually implicit relationships between the stress and the kinematical quantities. Another class of problems wherein it would be natural to develop implicit constitutive theories, though seldom resorted to, are models for bodies that are...

Curved composite beam with interlayer slip loaded by radial load

István Ecsedi, Ákos József Lengyel (2015)

Curved and Layered Structures

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Elastic two-layer curved composite beam with partial shear interaction is considered. It is assumed that each curved layer separately follows the Euler-Bernoulli hypothesis and the load slip relation for the flexible shear connection is a linear relationship. The curved composite beam at one of the end cross sections is fixed and the other end cross section is subjected by a concentrated radial load. Two cases are considered. In the first case the loaded end cross section is closed by...