Browsing by Author "Tran, Loc V."

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A geometrically nonlinear Euler–Bernoulli beam model within strain gradient elasticity with isogeometric analysis and lattice structure applications
(2020) Tran, Loc V.; Niiranen, Jarkko
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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 Cp-1-continuous B-spline 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.
Size-dependent nonlinear analysis and damping responses of FG-CNTRC micro-plates
(2019-08-15) Thanh, Cuong-Le; Tran, Loc V.; Vu-Huu, T.; Nguyen-Xuan, H.; Abdel-Wahab, M.
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
This paper presents a nonlinear numerical model, which is based on the modified couple stress theory (MCST), and trigonometric shear deformation theory coupled with isogeometric analysis. The present approach captures the small scale effects on the geometrically nonlinear behaviors of functionally graded carbon nanotube reinforced composite (FG-CNTRC) micro-plate with four patterns distribution. The equations of motion are established based on a Galerkin weak form associated with von-Kármán nonlinear strains. The MCST utilizes only one material length scale parameter to predict the size effect in FG-CNTRC micro-plate, for which its material properties are derived from an extended rule of mixture. The solutions of nonlinear static equation are obtained by using the Newton–Raphson technique and the Newmark time iteration procedure in association with Picard method is assigned to get responses of the nonlinear dynamic problems. In addition, the Rayleigh damping is applied to consider the influence of damping characteristic on the oscillation of FG-CNTRC micro-plates. Comparisons are performed to verify the proposed approach. Afterward, the numerical examples are used to show the effects of the distribution of carbon nanotubes (CNT), their volume fraction, the material length scale parameter and the boundary conditions on the nonlinear static and dynamic behaviors of FG-CNTRC micro-plates.