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Evaluation of a quasi-dynamic algorithm for soil consolidation problems
Published in G. Swoboda, Numerical Methods in Geomechanics Innsbruck 1988, 2017
D. Kovačićc, A. Szavits-Nossan
The dynamic relaxation procedure is applied to the solution of equilibrium equations. The concept of the dynamic relaxation technique is to extend the static problem to a fictitious dynamic problem by adding a suitably adopted inertial term to equilibrium equations and then extracting the kinetic energy from the system until the static equilibrium state is reached. The kinetic energy extraction is achieved by setting the velocity vector of the oscilating system to zero at each kinetic energy peak.
Transition of deformation mechanisms in nanotwinned single crystalline SiC
Published in Philosophical Magazine, 2019
Saeed Z. Chavoshi, Mark A. Tschopp, Paulo S. Branicio
Each sample is first energy minimised using the conjugate gradient method, followed by a dynamic relaxation at T = 300 K and P = 0 GPa for 30 ps under isothermal-isobaric (NPT) dynamics. Then, using the NPT ensemble and the Velocity Verlet algorithm with a time step of 1.0 fs, a homogeneous uniaxial strain loading at a constant engineering strain rate of is imposed in the y- or x-direction, for orthogonal or lateral loading, respectively. Zero normal stress conditions are applied in the other directions. For the shear deformation tests, samples are sheared along the xy and yz planes at a constant shear rate of under canonical (NVT) ensemble. Additional uniaxial deformation simulations at low strain rates, e.g. , as well as using large sample with the cubic length size of 50 nm, containing ∼atoms, led to the same mechanical response and deformation behaviour, see Figure S1 in Supplementary Material.
A nonlocal strain gradient model for nonlinear dynamic behavior of bi-directional functionally graded porous nanoplates on elastic foundations
Published in Mechanics Based Design of Structures and Machines, 2023
M. Esmaeilzadeh, M. E. Golmakani, M. Sadeghian
In this article, the dynamic response of FG porous nanoplates on elastic foundation has been studied. Utilizing the FSDT, the rule of mixtures and considering various porosity distributions, the governing equations are derived. For solving the problems, the kinetic dynamic relaxation (KDR) technique and Newmark integration are employed with finite-difference discretization approach to gain numeric outcomes. In order to validate the current results, comparison studies have been done with some references which show the validity and accuracy of the formulations and results. The roles of effective parameters including porosity coefficients, nonlocal and strain gradient parameters, grading indexes and various boundary conditions and Winkler-Pasternak foundations have been examined on dimensionless deflection. The most significant results are as follows:The strain gradient coefficient affects the variations of dimensionless deflection more noteworthy than the nonlocal parameter.In the uneven porosity model, the maximum deflection is smaller than the even pattern.The growth of gradient indexes in 2D FG porous nanoplate increases the maximum deflection.The elastic foundation in even porosity distribution affects deflection more markedly than uneven porosity.Good accuracy, low computational cost and the stability are the major characteristics of the present numeric methods.
Ritz method analysis of rectilinear orthotropic composite circular plates undergoing in-plane bending and torsional moments
Published in Mechanics of Advanced Materials and Structures, 2021
Valerio G. Belardi, Pierluigi Fanelli, Francesco Vivio
The paper by Salehi and Sobhani [34] regards the first-order shear deformable bending analysis of rectilinear orthotropic sector plates that can be further extended to the non-linear case. After the derivation of the governing differential equations, the solution is achieved through a methodology founded on the dynamic relaxation method and the finite difference discretization technique. The numerical case studies provide the action a uniform pressure acting on the mid-surface of the sector plate and different constraints on the external edge; the effect of different geometrical parameters and lay-ups is investigated.