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Main Title: Verification of strain gradient elasticity computation by analytical solutions
Author(s): Yang, Hua
Timofeev, Dmitry
Abali, B. Emek
Li, Baotong
Müller, Wolfgang H.
Type: Article
Abstract: As there are different computational methods for simulating problems in generalized mechanics, we present simple applications and their closed-form solutions for verifying a numerical implementation. For such a benchmark, we utilize these analytical solutions and examine three-dimensional numerical simulations by the finite element method (FEM) using IsoGeometric Analysis (IGA) with the aid of open source codes, called tIGAr, developed within the FEniCS platform. A study for the so-called wedge forces and double tractions help to comprehend their roles in the displacement solution as well as examine the significance by comparing to the closed form solutions for given boundary conditions. It is found that numerical results are in a good agreement with the analytical solutions if wedge forces and double tractions are considered. It is also presented how the wedge forces become necessary in order to maintain equilibrium in strain gradient materials.
Subject(s): analytical solutions
strain gradient elasticity
three-dimensional problems
Issue Date: 26-Jul-2021
Date Available: 17-Dec-2021
Is Part Of: 10.14279/depositonce-12553
Language Code: en
DDC Class: 620 Ingenieurwissenschaften und zugeordnete Tätigkeiten
Journal Title: ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik
Publisher: Wiley
Volume: 101
Issue: 12
Article Number: e202100023
Publisher DOI: 10.1002/zamm.202100023
EISSN: 1521-4001
ISSN: 0044-2267
TU Affiliation(s): Fak. 5 Verkehrs- und Maschinensysteme » Inst. Mechanik » FG Kontinuumsmechanik und Materialtheorie
Appears in Collections:Technische Universität Berlin » Publications

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