Concurrent coupling of peridynamics and classical elasticity for elastodynamic problems

Abstract Basic static boundary value problems of elasticity are considered for a semi-infinite curvilinear prism Ω = {ρ 0 < ρ < ρ 1, α 0 < α < α 1, 0 < 𝑧 < ∞} in generalized cylindrical coordinates ρ, α, 𝑧 with Lamé coefficients ℎ ρ = ℎ α = ℎ(ρ, α), ℎ𝑧 = 1. It is proved that the solution of some boundary value problems of elasticity can be reduced to the sum of solutions of other boundary value problems of elasticity. Besides its cognitive significance, this fact also enables one to solve some non-classical elasticity problems.

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Modeling of Size Effects in Bending of Perforated Cosserat Plates

Modelling and Simulation in Engineering ◽

10.1155/2017/5246197 ◽

2017 ◽

Vol 2017 ◽

pp. 1-19 ◽

Cited By ~ 1

Author(s):

Roman Kvasov ◽

Lev Steinberg

Keyword(s):

Finite Element ◽

Stress Concentration ◽

Numerical Study ◽

The Finite Element Method ◽

Classical Elasticity ◽

Element Analysis ◽

Plate Deformation ◽

The Finite Element Analysis ◽

Circular Holes ◽

Different Shapes

This paper presents the numerical study of Cosserat elastic plate deformation based on the parametric theory of Cosserat plates, recently developed by the authors. The numerical results are obtained using the Finite Element Method used to solve the parametric system of 9 kinematic equations. We discuss the existence and uniqueness of the weak solution and the convergence of the proposed FEM. The Finite Element analysis of clamped Cosserat plates of different shapes under different loads is provided. We present the numerical validation of the proposed FEM by estimating the order of convergence, when comparing the main kinematic variables with an analytical solution. We also consider the numerical analysis of plates with circular holes. We show that the stress concentration factor around the hole is less than the classical value, and smaller holes exhibit less stress concentration as would be expected on the basis of the classical elasticity.

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Two- Versus Three-Dimensional Classical Elasticity

Modern Mechanics and Mathematics - Microstructural Randomness and Scaling in Mechanics of Materials ◽

10.1201/9781420010275.ch5 ◽

2007 ◽

pp. 171-190

Keyword(s):

Three Dimensional ◽

Classical Elasticity

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Three-Dimensional Buckling Analysis of Functionally Graded Saturated Porous Rectangular Plates under Combined Loading Conditions

Applied Sciences ◽

10.3390/app112110434 ◽

2021 ◽

Vol 11 (21) ◽

pp. 10434

Author(s):

Faraz Kiarasi ◽

Masoud Babaei ◽

Kamran Asemi ◽

Rossana Dimitri ◽

Francesco Tornabene

Keyword(s):

Three Dimensional ◽

Functionally Graded ◽

Constitutive Law ◽

Combined Loading ◽

Rectangular Plates ◽

Loading Conditions ◽

Classical Elasticity ◽

Novel Approach ◽

Buckling Behavior ◽

Generalized Differential

The present work studies the buckling behavior of functionally graded (FG) porous rectangular plates subjected to different loading conditions. Three different porosity distributions are assumed throughout the thickness, namely, a nonlinear symmetric, a nonlinear asymmetric and a uniform distribution. A novel approach is proposed here based on a combination of the generalized differential quadrature (GDQ) method and finite elements (FEs), labeled here as the FE-GDQ method, while assuming a Biot’s constitutive law in lieu of the classical elasticity relations. A parametric study is performed systematically to study the sensitivity of the buckling response of porous structures, to different input parameters, such as the aspect ratio, porosity and Skempton coefficients, along with different boundary conditions (BCs) and porosity distributions, with promising and useful conclusions for design purposes of many engineering structural porous members.

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Modeling of Deformations in a Ring Shaped Workpiece Due to Chucking and Cutting Forces

Manufacturing ◽

10.1115/imece2002-39112 ◽

2002 ◽

Cited By ~ 1

Author(s):

John A. Malluck ◽

Shreyes N. Melkote

Keyword(s):

Finite Element ◽

Theoretical Model ◽

Finite Element Model ◽

Cutting Forces ◽

Element Model ◽

Outer Diameter ◽

Classical Elasticity ◽

Elastic Deformations ◽

The Finite Element Model ◽

Classical Elasticity Theory

This paper presents a theoretical model for predicting the elastic deformations of ring-type workpieces due to in-plane chucking and cutting forces applied in turning processes. The model is derived from classical elasticity theory for bending of thin rings. Experimental results are presented to verify the strengths and limitations of this model. The results from a finite element model are also presented for comparison. For the ring diameters and radial chucking loads considered in this work, it is shown that the theoretical model is accurate to within 11% of the measured radial deformations for rings with inner-to-outer diameter ratio (Din/Dout) of 0.881. The finite element model is shown to yield slightly better results. The applicability of the theoretical model is illustrated by using it to predict the surface error produced in turning of a ring.

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Love waves in a nonlocal elastic media with voids

Journal of Vibration and Control ◽

10.1177/1077546318824144 ◽

2019 ◽

Vol 25 (8) ◽

pp. 1470-1483 ◽

Cited By ~ 2

Author(s):

Gurwinderpal Kaur ◽

Dilbag Singh ◽

SK Tomar

Keyword(s):

Boundary Conditions ◽

Elastic Layer ◽

Love Wave ◽

Critical Frequency ◽

Elastic Solid ◽

Specific Model ◽

Elastic Media ◽

Present Formulation ◽

Classical Elasticity ◽

Coefficient Versus

The propagation of Love-type waves in a nonlocal elastic layer with voids resting over a nonlocal elastic solid half-space with voids has been studied. Dispersion relations are derived using appropriate boundary conditions of the model. It is found that there exist two fronts of Love-type surface waves that may travel with distinct speeds. The appearance of the second front is purely due to the presence of voids in layered media. Both fronts are found to be dispersive in nature and affected by the presence of the nonlocality parameter. The first front is found to be nonattenuating, independent of void parameters and analogous to the Love wave of classical elasticity, while the second front is attenuating and depends on the presence of void parameters. Each of the fronts is found to face a critical frequency above which it ceases to propagate. For a specific model, the variation of the phase speeds of both the fronts with frequency, nonlocality, voids and thickness parameters is shown graphically. Attenuation coefficient versus frequency for the second front has also been depicted separately. Some particular cases are deduced from the present formulation.

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