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#### Keywords

Limit analysis (ZK-MEW) equation Advanced analysis Antidotal Bayesian Beta-derivative Burger’s equation Caputo fractional derivative Cell-based smoothed three-node Mindlin plate element (CS-MIN3) Cohesive model Computer virus Constitutive model Convection-diffusion equation Convective heating Coolant#### Institution

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- Vietnamese-German University 4 (%)
- University of Liège 3 (%)
- National University of Singapore 2 (%)
- Ton Duc Thang University 2 (%)
- VNUHCM International University 2 (%)

#### Author

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- Atangana, Abdon 2 (%)
- Bonyah, Ebenezer 2 (%)
- Canh, Le-Van 2 (%)
- Hung, Nguyen Dang 2 (%)
- Khan, Muhammad Altaf 2 (%)

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## RETRACTED ARTICLE: A limit analysis of Mindlin plates using the cell-based smoothed triangular element CS-MIN3 and second-order cone programming (SOCP)

### Asia Pacific Journal on Computational Engineering (2014-04-29) 1: 1-26 , April 29, 2014

### Background

The paper presents a numerical procedure for kinematic limit analysis of Mindlin plate governed by von Mises criterion.

### Methods

The cell-based smoothed three-node Mindlin plate element (CS-MIN3) is combined with a second-order cone optimization programming (SOCP) to determine the upper bound limit load of the Mindlin plates. In the CS-MIN3, each triangular element will be divided into three sub-triangles, and in each sub-triangle, 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 sub-triangles. 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.

## Retraction Note to: A limit analysis of Mindlin plates using the cell-based smoothed triangular element CS-MIN3 and second-order cone programming (SOCP)

### Asia Pacific Journal on Computational Engineering (2015-08-21) 2: 1 , August 21, 2015

## Upper bound limit analysis of plates using a rotation-free isogeometric approach

### Asia Pacific Journal on Computational Engineering (2014-08-27) 1: 1-29 , August 27, 2014

### Background

This paper presents a simple and effective formulation based on a rotation-free 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 B-splines or non-uniform rational B-splines (NURBS), resulting in both exactly geometric representation and high-order 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 large-scale plate problems. The optimization formulation of limit analysis is transformed into the form of a second-order cone programming problem so that it can be solved using highly efficient interior-point solvers.

### Results and conclusions

Several numerical examples are given to demonstrate reliability and effectiveness of the present method in comparison with other published methods.

## Modelling of shear localization in solids by means of energy relaxation

### Asia Pacific Journal on Computational Engineering (2014-05-12) 1: 1-21 , May 12, 2014

An approach to the problem of shear localization is proposed. It is based on energy minimization principles associated with micro-structure developments. Shear bands are treated as laminates of first order. The micro-shear band is assumed to have a zero thickness, leading to an unbounded strain field and the special form of the energy within this micro-band. The energy is approximated by the mixture of potential of two low-strain and high-strain domains and it is non-convex. The problem of the non-convex energy arising due to the formation of shear bands is solved by energy relaxation in order to ensure that the corresponding problem is well-posed. 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.

## FEM-based shakedown analysis of hardening structures

### Asia Pacific Journal on Computational Engineering (2014-04-29) 1: 1-13 , April 29, 2014

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 two-surface 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 back-stress 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.

## Modeling the spread of computer virus via Caputo fractional derivative and the beta-derivative

### Asia Pacific Journal on Computational Engineering (2017-01-03) 4: 1-15 , January 03, 2017

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 well-recognized 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 beta-derivatives. 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.

## Model order reduction for Bayesian approach to inverse problems

### Asia Pacific Journal on Computational Engineering (2014-04-29) 1: 1-17 , April 29, 2014

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 reduced-order model and a Bayesian inference formulation to rapidly determine contaminant locations given sparse measurements of contaminant concentration. The system is modelled by the coupled Navier-Stokes equations and convection-diffusion transport equations. The Galerkin finite element method provides an approximate numerical solution-the ’full model’, which cannot be solved in real-time. The proper orthogonal decomposition and Galerkin projection technique are applied to obtain a reduced-order 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 reduced-order model to the source inversion problem yields a speed-up 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.

## Traveling wave solutions of Zakharov–Kuznetsov-modified equal-width and Burger’s equations via $$ {\text{exp}}( - \varphi \left( \eta \right)) $$ exp ( - φ η ) -expansion method

### Asia Pacific Journal on Computational Engineering (2015-10-07) 2: 1-10 , October 07, 2015

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–Kuznetsov-modified equal-width (ZK-MEW) 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.

## Editorial: Asia Pacific Journal on Computational Engineering

### Asia Pacific Journal on Computational Engineering (2014-04-29) 1: 1-2 , April 29, 2014

## Plastic collapse mechanisms in thin disks subject to thermo-mechanical loading

### Asia Pacific Journal on Computational Engineering (2014-04-29) 1: 1-9 , April 29, 2014

### Background

A new solution for plastic collapse of a thin annular disk subject to thermo-mechanical loading is presented.

### Methods

It is assumed that plastic yielding is controlled by Hill's quadratic orthotropic yield criterion. A distinguished feature of the boundary value problem considered is that there are two loading parameters. One of these parameters is temperature, and the other is pressure over the inner radius of the disk.

### Results

The general qualitative structure of the solution at plastic collapse is discussed in detail.

### Conclusions

It is shown that two different plastic collapse mechanisms are possible. One of these mechanisms is characterized by strain localization at the inner radius of the disk. The entire disk becomes plastic according to the other collapse mechanism. In addition, two special regimes of plastic collapse are identified. According to one of these regimes, plastic collapse occurs when the entire disk is elastic except its inner radius. According to the other regime, the entire disk becomes plastic at the same values of the loading parameters at which plastic yielding starts to develop.