An Efficient Technique in Shape Optimization*, †

A shape optimization method is presented for smoothing stress peaks that are caused by notch effects on unloaded edges of holes in plates or shell structures with linear-elastic, homogeneous, isotropic material under external forces. The optimization problem is first formulated as a functional whose integrand contains the difference between the stresses at the hole edge and the optimal stress. This mechanical problem is approximated by a sequence of purely geometric, substitute functionals. The substitute functional is discretized by means of splines and formulated as a nonlinear constrained optimization problem which is solved with a quasi-Newton method. The efficiency of the method is demonstrated on the basis of examples.     

Optimal Synthesis of Frameworks under Elastic and Plastic Performance Constraints Using Discrete Sections *, †

ABSTRACT

A computer-based method is presented for minimum-weight design of planar frameworks under service and ultimate performance conditions using discrete member sections. Service-load conditions ensure acceptable elastic stresses and displacements, and ultimate-load conditions ensure adequate safety against plastic collapse. The sizes of the discrete sections, which can be of any type; e.g., WF, HSS, etc., may be constrained to satisfy fabrication requirements related to member continuity and structure symmetry. The design method is iterative in nature and remarkably efficient. The number of iterations is generally small and almost totally independent of the complexity of the structure. Several comparative designs for simple truss and frame structures are presented to illustrate features of the method.     

The Minimal Thickness of a Semicircular Arch with a Tension-Free Crown∗

ABSTRACT

When a semicircular elastic arch is loaded with a single point force at the vertex, the stress at interior points depends on the thickness of the arch and on the way the abutments react. Applying the theory of plane elasticity, three typical load-bearing abutment constraints are evaluated to find the minimal thickness at which no tensile stress occurs at a given interior point. Such thickness is found to be quite large.     

Existence of Solutions with the Prescribed Flux of the Navier–Stokes System in an Infinite Cylinder

The existence and uniqueness of a solution to the nonstationary Navier–Stokes system having a prescribed flux in an infinite cylinder is proved. We assume that the initial data and the external forces do not depend on x₃ and find the solution (u, p) having the following form

Development and Validation of a Numerical Model of Flow Through Embankment Dams – Comparisons with Experimental Data and Analytical Solutions

The development and validation of a numerical simulation model of the flow through embankment dams is described. The paper focuses on basic verification studies, that is, comparisons with analytical solutions and data from laboratory experiments. Two experimental studies, one dealing with the flow in a Hele–Shaw cell and the other with the flow through a bed of packed glass beads, are also described. Comparisons are carried out with respect to the phreatic surfaces, pressure profiles, seepage levels and discharges. It is concluded that the agreement between experimental, analytical and numerical results is generally satisfactory.     

The Explicit Forms of Field Functions in Totrahedron Element with 16 and 20 Degrees of Freedom

In this paper,the explicit forms of field functions in tetrehedron elements with16 and20degrees of freedom are given in terms of volume coordinates L_1,L_2,L_3,L_4 of tetrahedron.     

Well-Posedness for Multicomponent Schrödinger–gKdV Systems and Stability of Solitary Waves with Prescribed Mass

In this paper we prove the well-posedness issues of the associated initial value problem, the existence of nontrivial solutions with prescribed \(L^2\)-norm, and the stability of associated solitary waves for two classes of coupled nonlinear dispersive equations. The first problem here describes the nonlinear interaction between two Schrödinger type short waves and a generalized Korteweg-de Vries type long wave and the second problem describes the nonlinear interaction of two generalized Korteweg-de Vries type long waves with a common Schrödinger type short wave. The results here extend many of the previously obtained results for two-component coupled Schrödinger–Korteweg-de Vries systems.     

Three-Dimensional Lattice Boltzmann Simulations of Single-Phase Permeability in Random Fractal Porous Media with Rough Pore–Solid Interface

Single-phase permeability k has intensively been investigated over the past several decades by means of experiments, theories and simulations. Although the effect of surface roughness on fluid flow and permeability in single pores and fractures as well as networks of fractures was studied previously, its influence on permeability in a random mass fractal porous medium constructed of pores of different sizes remained as an open question. In this study, we, therefore, address the effect of pore–solid interface roughness on single-phase flow in random fractal porous media. For this purpose, we apply a mass fractal model to construct porous media with a priori known mass fractal dimensions \(2.579 \le D_{\mathrm{m}} \le 2.893\) characterizing both solid matrix and pore space. The pore–solid interface of the media is accordingly roughened using the Weierstrass–Mandelbrot approach and two parameters, i.e., surface fractal dimension \(D_{\mathrm{s}}\) and root-mean-square (rms) roughness height. A single-relaxation-time lattice Boltzmann method is applied to simulate single-phase permeability in the corresponding porous media. Results indicate that permeability decreases sharply with increasing \(D_{\mathrm{s}}\) from 1 to 1.1 regardless of \(D_{\mathrm{m}}\) value, while k may slightly increase or decrease, depending on \(D_{\mathrm{m}}\), as \(D_{\mathrm{s}}\) increases from 1.1 to 1.6.     

Optimization of the numerical treatment of the Darcy–Forchheimer flow of Ree–Eyring fluid with chemical reaction by using artificial neural networks

In this study, Darcy Forchheimer flow paradigm, which is a useful paradigm in fields such as petroleum engineering where high flow velocity effects are common, has been analyzed with artificial intelligence approach. In this context, first of all, Darcy–Forchheimer flow of Ree–Eyring fluid along a permeable stretching surface with convective boundary conditions has been examined and heat and mass transfer mechanisms have been investigated by including the effect of chemical process, heat generation/absorption, and activation energy. Cattaneo–Christov heat flux model has been used to analyze heat transfer properties. Within the scope of optimizing Darcy–Forchheimer flow of Ree–Eyring fluid; three different artificial neural network models have been developed to predict Nusselt number, Sherwood number, and skin friction coefficient values. The developed artificial neural network model has been able to predict Nusselt number, Sherwood number, and skin friction coefficient values with high accuracy. The findings obtained as a result of the study showed that artificial neural networks are an ideal tool that can be used to model Darcy–Forchheimer Ree–Eyring fluid flow towards a permeable stretch layer with activation energy and a convective boundary condition.     

Shape analysis and damped oscillatory solutions for a class of nonlinear wave equation with quintic term简

This paper aims at analyzing the shapes of the bounded traveling wave solu- tions for a class of nonlinear wave equation with a quintic term and obtaining its damped oscillatory solutions. The theory and method of planar dynamical systems are used to make a qualitative analysis to the planar dynamical system which the bounded traveling wave solutions of this equation correspond to. The shapes, existent number, and condi- tions are presented for all bounded traveling wave solutions. The bounded traveling wave solutions are obtained by the undetermined coefficients method according to their shapes, including exact expressions of bell and kink profile solitary wave solutions and approxi- mate expressions of damped oscillatory solutions. For the approximate damped oscillatory solution, using the homogenization principle, its error estimate is given by establishing the integral equation, which reflects the relation between the exact and approximate so- lutions. It can be seen that the error is infinitesimal decreasing in the exponential form.