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By
Trung, NguyenThoi; Phuc, PhungVan; Canh, LeVan
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1 Citations
Background
The paper presents a numerical procedure for kinematic limit analysis of Mindlin plate governed by von Mises criterion.
Methods
The cellbased smoothed threenode Mindlin plate element (CSMIN3) is combined with a secondorder cone optimization programming (SOCP) to determine the upper bound limit load of the Mindlin plates. In the CSMIN3, each triangular element will be divided into three subtriangles, and in each subtriangle, the gradient matrices of MIN3 is used to compute the strain rates. Then the gradient smoothing technique on whole the triangular element is used to smooth the strain rates on these three subtriangles. The limit analysis problem of Mindlin plates is formulated by minimizing the dissipation power subjected to a set of constraints of boundary conditions and unitary external work. For Mindlin plates, the dissipation power is computed on both the middle plane and thickness of the plate. This minimization problem then can be transformed into a form suitable for the optimum solution using the SOCP.
Results and Conclusions
The numerical results of some benchmark problems show that the proposal procedure can provide the reliable upper bound collapse multipliers for both thick and thin plates.
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By
NguyenXuan, Hung; Thai, Chien Hoang; Bleyer, Jeremy; Nguyen, Phu Vinh
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1 Citations
Background
This paper presents a simple and effective formulation based on a rotationfree isogeometric approach for the assessment of collapse limit loads of plastic thin plates in bending.
Methods
The formulation relies on the kinematic (or upper bound) theorem and namely Bsplines or nonuniform rational Bsplines (NURBS), resulting in both exactly geometric representation and highorder approximations. Only one deflection variable (without rotational degrees of freedom) is used for each control point. This allows us to design the resulting optimization problem with a minimum size that is very useful to solve largescale plate problems. The optimization formulation of limit analysis is transformed into the form of a secondorder cone programming problem so that it can be solved using highly efficient interiorpoint solvers.
Results and conclusions
Several numerical examples are given to demonstrate reliability and effectiveness of the present method in comparison with other published methods.
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By
Trinh, Tuyet B; Hackl, Klaus
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An approach to the problem of shear localization is proposed. It is based on energy minimization principles associated with microstructure developments. Shear bands are treated as laminates of first order. The microshear band is assumed to have a zero thickness, leading to an unbounded strain field and the special form of the energy within this microband. The energy is approximated by the mixture of potential of two lowstrain and highstrain domains and it is nonconvex. The problem of the nonconvex energy arising due to the formation of shear bands is solved by energy relaxation in order to ensure that the corresponding problem is wellposed. An application of the proposed formulation to isotropic material is presented. The capability of the proposed concept is demonstrated through numerical simulation of a tension test.
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By
Phạm, Phú Tình; Staat, Manfred
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3 Citations
This paper develops a new finite element method (FEM)based upper bound algorithm for limit and shakedown analysis of hardening structures by a direct plasticity method. The hardening model is a simple twosurface model of plasticity with a fixed bounding surface. The initial yield surface can translate inside the bounding surface, and it is bounded by one of the two equivalent conditions: (1) it always stays inside the bounding surface or (2) its centre cannot move outside the backstress surface. The algorithm gives an effective tool to analyze the problems with a very high number of degree of freedom. Our numerical results are very close to the analytical solutions and numerical solutions in literature.
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By
Bonyah, Ebenezer; Atangana, Abdon; Khan, Muhammad Altaf
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1 Citations
The concept of information science is inevitable in the human development as science and technology has become the driving force of all economics. The connection of one human being during epidemics is vital and can be studied using mathematical principles. In this study, a wellrecognized model of computer virus by Piqueira et al. (J Comput Sci 1:31−34, 2005) and Piqueira and Araujo (Appl Math Comput 2(213):355−360, 2009) is investigated through the Caputo and betaderivatives. A less detail of stability analysis was discussed on the extended model. The analytical solution of the extended model was solved via the Laplace perturbation method and the homotopy decomposition technique. The sequential summary of each of iteration method for the extend model was presented. Using the parameters in Piqueira and Araujo (Appl Math Comput 2(213):355−360, 2009), some numerical simulation results are presented.
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By
Nguyen, NgocHien; Cheong Khoo, Boo; Willcox, Karen
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1 Citations
This work presents an approach to solve inverse problems in the application of water quality management in reservoir systems. One such application is contaminant cleanup, which is challenging because tasks such as inferring the contaminant location and its distribution require large computational efforts and data storage requirements. In addition, real systems contain uncertain parameters such as wind velocity; these uncertainties must be accounted for in the inference problem. The approach developed here uses the combination of a reducedorder model and a Bayesian inference formulation to rapidly determine contaminant locations given sparse measurements of contaminant concentration. The system is modelled by the coupled NavierStokes equations and convectiondiffusion transport equations. The Galerkin finite element method provides an approximate numerical solutionthe ’full model’, which cannot be solved in realtime. The proper orthogonal decomposition and Galerkin projection technique are applied to obtain a reducedorder model that approximates the full model. The Bayesian formulation of the inverse problem is solved using a Markov chain Monte Carlo method for a variety of source locations in the domain. Numerical results show that applying the reducedorder model to the source inversion problem yields a speedup in computational time by a factor of approximately 32 with acceptable accuracy in comparison with the full model. Application of the inference strategy shows the potential effectiveness of this computational modeling approach for managing water quality.
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By
MohyudDin, Syed Tauseef; Ali, Ayyaz; Iqbal, Muhammad Asad
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In this article, a technique is proposed for obtaining better and accurate results for nonlinear PDEs. We constructed abundant exact solutions via exp
$$ (  \varphi \left( \eta \right)) $$
expansion method for the Zakharov–Kuznetsovmodified equalwidth (ZKMEW) equation and the (2 + 1)dimensional Burgers equation. The traveling wave solutions are found through the hyperbolic functions, the trigonometric functions and the rational functions. The specified idea is very pragmatic for PDEs, and could be extended to engineering problems.
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