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Abstract
The nonlinear governing differential equation and variational formulation of the Euler–Bernoulli beam model are formulated within Mindlin’s strain gradient elasticity theory of form II by adopting the von Kármán strain assumption. The formulation can retrieve some simplified beam models of generalized elasticity such as the models of simplified strain gradient theory (SSGT), modified strain gradient theory (MSGT), and modified couple stress theory (MCST). Without the presence of nonlinear terms, the resulting linear differential equation is solvable by analytical means, whereas the mathematical complexity of the nonlinear problem is treated with the Newton–Raphson iteration and a conforming isogeometric Galerkin method with C^{p}^{1}continuous Bspline basis functions of order p ≥ 3. Through a set of numerical examples, the accuracy and validity of the present theoretical formulation at linear and nonlinear regimes are confirmed. Finally, an application to lattice frame structures illustrates the benefits of the present beam model in saving computational costs, while maintaining high accuracy as compared to standard 2D finite element simulations.
Original language  English 

Pages (fromto)  345371 
Number of pages  27 
Journal  Mathematics and Mechanics of Complex Systems 
Volume  8 
Issue number  4 
DOIs  
Publication status  Published  2020 
MoE publication type  A1 Journal articlerefereed 
Keywords
 beam model
 geometric nonlinearity
 isogeometric analysis
 lattice structure
 strain gradient elasticity
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Projects
 1 Finished

Isogeometric adaptive methods for thinwalled structures– with applications from architectural and industrial design in structural and mechanical engineering
Balobanov, V., Shahzad, S., Niiranen, J., Khakalo, S. & Nguyen, T.
01/09/2016 → 31/08/2018
Project: Academy of Finland: Other research funding