Limit analysis decomposition and finite element mixed method

This paper proposes an original decomposition approach to the upper bound method of limit analysis. It is based on a mixed finite element approach and on a convex interior point solver, using linear or quadratic discontinuous velocity fields. Presented in plane strain, this method appears to be rapidly convergent, as verified in the Tresca compressed bar problem in the linear velocity case. Then, using discontinuous quadratic velocity fields, the method is applied to the celebrated problem of the stability factor of a Tresca vertical slope: the upper bound is lowered to 3.7776-value to be compared to the best published lower bound 3.7752-by succeeding in solving a nonlinear optimization problem with millions of variables and constraints.     

Shape design sensitivity analysis of plates and plane elastic solids under unilateral constraints

The local dependence of static response and eigenvalues on the shape of plates and plane elastic solids is characterized. The so-called material derivative method is used. The shape sensitivity analysis includes, besides linear problems, nonlinear problems with unilateral conditions, e.g., the frictionless contact problem for an elastic body on a rigid foundation. The results on shape sensitivity analysis can be used to obtain expressions for variations of integral functionals that arise in structural optimization problems.The authors are indebted to Professor N. Olhoff and Dr. M. P. Bendsøe for stimulating discussions and valuable comments on design sensitivity analysis.     

A measure of independence for a multivariate normal distribution and some connections with factor analysis

This paper gives results for the population value of a measure of the goodness-of-fit of a general multivariate normal distribution to the simpler hypothesis of independent normal variables. The measure was introduced by Rudas, Clogg and Lindsay in 1994, who gave the value for the bivariate normal distribution. Connections with factor analysis are briefly discussed.     

Coupling of numerical Green''s matrix and boundary integral equations for the elastodynamic analysis of inhomogeneous bodies on an elastic half-space

A coupled system of integral equations (of the domain and boundary types) is formulated for the elastodynamic response analysis of a locally inhomogeneous body on a homogeneous elastic half-space. The method uses the fundamental solution for homogeneous elastostatics in the inhomogeneous domain owing to the lack of a fundamental solution in inhomogeneous elastodynamics.

The integral representation of displacements in the inhomogeneous domain is formulated with the help of this elastostatic fundamental solution by considering the term induced by the inhomogeneity of materials and the acceleration term as the body force term. Then the Green's matrix is obtained numerically from this integral representation and combined with the ordinary boundary integral equations, which are valid in the exterior homogeneous half-space.

Some numerical examples show the efficiency and the versatility of this coupled method.     

An integrated numerical method with error analysis for solving fractional differential equations of quintic nonlinear type arising in applied sciences

In this study, fractional differential equations having quintic nonlinearity are considered by proposing an accurate numerical method based on the matching polynomial and matrix‐collocation system. This method provides an integration between matrix and fractional derivative, which makes it fast and efficient. A hybrid computer program is designed by making use of the fast algorithmic structure of the method. An error analysis technique consisting of the fractional‐based residual function is constructed to scrutinize the precision of the method. Some error tests are also performed. Figures and tables present the consistency of the approximate solutions of highly stiff model problems. All results point out that the method is effective, simple, and eligible.     

Finite element analysis and modeling of structure with bolted joints

In this work, in order to investigate a modeling technique of the structure with bolted joints, four kinds of finite element models are introduced; a solid bolt model, a coupled bolt model, a spider bolt model, and a no-bolt model. All the proposed models take into account pretension effect and contact behavior between flanges to be joined. Among these models, the solid bolt model, which is modeled by using 3D solid elements and surface-to-surface contact elements between head/nut and the flange interfaces, provides the best accurate responses compared with the experimental results. In addition, the coupled bolt model, which couples degree of freedom between the head/nut and the flange, shows the best effectiveness and usefulness in view of computational time and memory usage. Finally, the bolt model proposed in this study is adopted for a structural analysis of a large marine diesel engine consisting of several parts which are connected by long stay bolts.     

Non-probabilistic convex models and interval analysis method for dynamic response of a beam with bounded uncertainty

This paper is concerned with the comparison of two non-probabilistic set-theoretical models for dynamic response measures of an infinitely long beam. The beam is on an uncertain foundation and subjected to a moving force with constant speed. The steady state vibration is analyzed with finite element method. The dynamic responses of the beam are approximated to the first-order respect of the uncertainty variables. As a rule, in convex models and interval analysis, the uncertainties are considered to be unknown, but they give out their allowable vector space. Comparing the convex models with interval analysis in mathematical proofs and numerical calculations, it’s shows that under the condition of transform an interval vector to an outer enclosed ellipsoid, the dynamic response of the infinitely long beam predicted by interval analysis is smaller than that by convex models; under the condition of transform a hyperellipsoid to an outer enclosed interval vector, the dynamic response of the infinitely long beam calculated by convex models is smaller than that by interval analysis method.     

Similarity solution of boundary layer stagnation-point flow towards a heated porous stretching sheet saturated with a nanofluid with heat absorption/generation and suction/blowing: A Lie group analysis

In this paper, heat and mass transfer analysis for boundary layer stagnation-point flow over a stretching sheet in a porous medium saturated by a nanofluid with internal heat generation/absorption and suction/blowing is investigated. The governing partial differential equation and auxiliary conditions are converted to ordinary differential equations with the corresponding auxiliary conditions via Lie group analysis. The boundary layer temperature, concentration and nanoparticle volume fraction profiles are then determined numerically. The influences of various relevant parameters, namely, thermophoresis parameter Nt, Brownian motion parameter Nb, Lewis number Le, suction/injection parameter S, permeability parameter k₁, source/sink parameter λ and Prandtl parameter Pr on temperature and concentration as well as wall heat flux and wall mass flux are discussed. Comparison with published results is presented.     

Non-linear analysis of the consolidation of an elastic saturated soil with incompressible fluid and variable permeability by FEM

Research interest in the mechanical behaviour of soils is growing as a result of an increasing number of geomechanical problems involving consolidation effects. The main aim of this paper is to validate and to solve a model for consolidation of an elastic saturated soil with incompressible fluid and variable permeability. Firstly, we prove the existence and uniqueness of the solution of the variational problem corresponding to an initial and boundary value problem (IBVP): a special case of the Biot’s ‘consolidation of clay’ model (where the applied forces depend on time). Secondly, we prove the convergence of the method using a technique based on the proof of solution’s existence. Finally, we then solved this constitutive model by the finite element method (FEM) employing repeated fixed point techniques in order to obtain the results for displacement and pore water pressure. The pore fluid is considered incompressible. The results of the numerical experiments are compared with analytical solutions and, in cases where such solutions do not exist, with experimental data. Therefore, the model can be used for quantitative predictions of consolidation behaviour of soils with permeability dependent on the settlement.     

Mathematical analysis and numerical simulation of chaotic noninteger order differential systems with Riemann‐Liouville derivative

This article deals with the design, analysis, and implementation of a robust numerical scheme when applied to time‐fractional reaction‐diffusion system. Stability analysis and numerical treatment of chaotic fractional differential system in Riemann‐Liouville sense are considered in this article. Simulation results show that chaotic phenomena can only occur if the reaction or local dynamics of such system is coupled or nonlinear in nature. Illustrative examples that are still of current and recurring interest to economists, engineers, mathematicians and physicists are chosen, to describe the points and queries that may arise. Numerical results presented agree with the theoretical findings.     

Reliability analysis and optimization of weighted voting systems with continuous states input

Weighted voting systems are widely used in many practical fields such as target detection, human organization, pattern recognition, etc. In this paper, a new model for weighted voting systems with continuous state inputs is formulated. We derive the analytical expression for the reliability of the entire system under certain distribution assumptions. A more general Monte Carlo algorithm is also given to numerically analyze the model and evaluate the reliability. This paper further proposes a reliability optimization problem of weighted voting systems under cost constraints. A genetic algorithm is introduced and applied as the optimization technique for the model formulated. A numerical example is then presented to illustrate the ideas.     

Comparative analysis of the machine repair Problem with imperfect coverage and service pressure condition

In this paper we analyze the warm-standby M/M/R machine repair problem with multiple imperfect coverage which involving the service pressure condition. When an operating machine (or warm standby) fails, it may be immediately detected, located, and replaced with a coverage probability c by a standby if one is available. We use a recursive method to develop the steady-state analytic solutions which are used to calculate various system performance measures. The total expected profit function per unit time is derived to determine the joint optimal values at the maximum profit. We first utilize the direct search method to measure the various characteristics of the profit function followed by Quasi-Newton method to search the optimal solutions. Furthermore, the particle swarm optimization (PSO) algorithm is implemented to find the optimal combinations of parameters in the pursuit of maximum profit. Finally, a comparative analysis of the Quasi-Newton method with the PSO algorithm has demonstrated that the PSO algorithm provides a powerful tool to perform the optimization problem.     

Falsification of hybrid systems with symbolic reachability analysis and trajectory splicing

The falsification of a hybrid system aims at finding trajectories that violate a given safety property. This is a challenging problem, and the practical applicability of current falsification algorithms still suffers from their high time complexity. In contrast to falsification, verification algorithms aim at providing guarantees that no such trajectories exist. Recent symbolic reachability techniques are capable of efficiently computing linear constraints that enclose all trajectories of the system with reasonable precision. In this paper, we leverage the power of symbolic reachability algorithms to improve the scalability of falsification techniques. Recent approaches to falsification reduce the problem to a nonlinear optimization problem. We propose to reduce the search space of the optimization problem by adding linear state constraints obtained with a reachability algorithm. An empirical study of how varying abstractions during symbolic reachability analysis affect the performance of solving a falsification problem is presented. In addition, for solving a falsification problem, we propose an alternating minimization algorithm that solves a linear programming problem and a non-linear programming problem in alternation finitely many times. We showcase the efficacy of our algorithms on a number of standard hybrid systems benchmarks demonstrating the performance increase and number of falsifyable instances.