Nonlocal gradient integral models with a bi-Helmholtz averaging kernel for functionally graded beams

DOI10.1016/j.apm.2022.03.013zbMath1503.74072OpenAlexW4220693060WikidataQ114208665 ScholiaQ114208665MaRDI QIDQ2109577

Hai Qing, Pei Zhang, Peter Schiavone

Publication date: 21 December 2022

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apm.2022.03.013

zbMATH Keywords

Laplace transformconstitutive boundary conditionsbi-Helmholtz averaging kernelFG beamsnonlocal gradient integral models

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Averaging of perturbations for nonlinear problems in mechanics (70K65)

Cites Work

• A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation
• Nonlocal theories for bending, buckling and vibration of beams
• Higher-order nonlocal gradient elasticity: a consistent variational theory
• One-dimensional stress-driven nonlocal integral model with bi-Helmholtz kernel: close form solution and consistent size effect
• Applying nonlocal strain gradient theory to size-dependent analysis of functionally graded carbon nanotube-reinforced composite nanoplates
• Torsional static and vibration analysis of functionally graded nanotube with bi-Helmholtz kernel based stress-driven nonlocal integral model
• Experiments and theory in strain gradient elasticity.
• Closed form solution for a nonlocal strain gradient rod in tension
• Integro-differential nonlocal theory of elasticity
• Constitutive boundary conditions for nonlocal strain gradient elastic nano-beams
• Free vibrations of elastic beams by modified nonlocal strain gradient theory
• Nonlinear bending and free vibration analyses of nonlocal strain gradient beams made of functionally graded material
• Nonlocal elasticity in nanobeams: the stress-driven integral model
• Buckling analysis of Euler-Bernoulli beams using Eringen's two-phase nonlocal model
• A strain gradient functionally graded Euler-Bernoulli beam formulation
• Stress-driven nonlocal integral model for Timoshenko elastic nano-beams
• A research into bi-Helmholtz type of nonlocal elasticity and a direct approach to Eringen's nonlocal integral model in a finite body
• Couple stress based strain gradient theory for elasticity
• The nonlocal frequency behavior of nanomechanical mass sensors based on the multi-directional vibrations of a buckled nanoribbon
• Variationally consistent dynamics of nonlocal gradient elastic beams
• Theoretical analysis on elastic buckling of nanobeams based on stress-driven nonlocal integral model
• Limit behaviour of Eringen's two-phase elastic beams
• Non-standard and constitutive boundary conditions in nonlocal strain gradient elasticity
• Influence of homogenization models on size-dependent nonlinear bending and postbuckling of bi-directional functionally graded micro/nano-beams
• Iterative methods for nonlocal elasticity problems
• Nonlinear vibration analysis of FG nano-beams resting on elastic foundation in thermal environment using stress-driven nonlocal integral model
• Surface effects on the buckling behaviors of piezoelectric cylindrical nanoshells using nonlocal continuum model
• A unified size-dependent plate model based on nonlocal strain gradient theory including surface effects
• Variational nonlocal gradient elasticity for nano-beams
• On nonlocal mechanics of curved elastic beams
• On the consistency of the nonlocal strain gradient elasticity
• On a theory of nonlocal elasticity of bi-Helmholtz type and some applications
• Elasticity theory of materials with long range cohesive forces
• Linear theory of nonlocal elasticity and dispersion of plane waves
• On nonlocal elasticity
• Micro-structure in linear elasticity
• Exact solutions for size-dependent bending of Timoshenko curved beams based on a modified nonlocal strain gradient model
• Exact solutions for the bending of Timoshenko beams using Eringen’s two-phase nonlocal model

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