Matrices in Engineering Problems

In the process of the rapid development of science and technology, people study many problems with the help of the independent variables, but the according descriptions have not been accurate enough. Therefore, many problems must be described by a function of more than one variable to more accurately get the results that people need to use the functions containing more than one variable and their partial derivatives to study the real problems of the method. Partial differential equations are closely and directly related to many problems in physics, mechanics, and engineering. It becomes an important bridge between mathematical theory and practical problems in physics, mechanics, and engineering. And the elements in Hilbert space, vectors, can represent vectors, functions, and phase quantities, while the special solutions of partial differential equations in solving physical problems can satisfy the common properties of Hilbert space. The analogy of functions and phase quantities to vectors can establish the function space and phase quantity space with geometric intuition. Based on Hilbert space theory, the key and difficult problems in engineering management can be explained by clear mathematical models by using the analogy method. The purpose of this study is to enrich the means of the building engineering management model, to broaden the horizon of managers, and to solve the problems in engineering management from a new dimension.

For various scientific and engineering problems, how to deal with variables and parameters of uncertain value is an important issue. Full analysis of the specific errors in measurement, observations, experiments, and applications are vital in dealing with the parameters taken to simplify the problem. Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems aims to provide the reader with basic concepts for soft computing and other methods for various means of uncertainty in handling solutions, analysis, and applications. This book is an essential reference work for students, scholars, practitioners and researchers in the assorted fields of engineering and applied mathematics interested in a model for uncertain physical problems.

Chaos in dynamical systems is still considered to be a somewhat curious, and generally undesirable property of non-linear systems. Despite the plethora of chaotic control methods published over the last decades, only in a few instances has the control of chaos been used to address real world problems in engineering or medicine. This is partly due to the limits of the used control methods, which either require specific analytical knowledge of the system, or the system needs to have specific characteristics to be able to be controllable. The lack of solutions for engineering and biomedical problems may also be due to specific requirements that prevent the implementation of control methods and the, as yet unproven, benefits that controlled chaos may bring to these problems. The aim of a practical application of chaos control is to fully control chaos in theoretical problems first, and then show applicable solutions to physical problems of stability and control. This controlled chaotic state should then have clear and distinct dynamic advantages over uncontrolled chaos and steady state systems. The application of the Rate Control of Chaos (RCC) method, which is derived from metabolic control processes, has already been shown to be effective in controlling several engineering problems. RCC allows non-linear systems to be stabilised into controlled oscillations, even across bifurcations, and it also allows the system to operate in regions of the parameter space that are inaccessible without this method of control. For fun, I will show that RCC controls the N-Body problem; for profit, it can control a bioreactor model to greatly improve yield. The RCC method promises to, finally, permit the control of complex dynamic systems.

Comprehensive Coverage of the New, Easy-to-Learn C# Although C, C++, Java, and Fortran are well-established programming languages, the relatively new C# is much easier to use for solving complex scientific and engineering problems. Numerical Methods, Algorithms and Tools in C# presents a broad collection of practical, ready-to-use mathematical routines employing the exciting, easy-to-learn C# programming language from Microsoft. The book focuses on standard numerical methods, novel object-oriented techniques, and the latest Microsoft .NET programming environment. It covers complex number functions, data sorting and searching algorithms, bit manipulation, interpolation methods, numerical manipulation of linear algebraic equations, and numerical methods for calculating approximate solutions of non-linear equations. The author discusses alternative ways to obtain computer-generated pseudo-random numbers and real random numbers generated by naturally occurring physical phenomena. He also describes various methods for approximating integrals and special functions, routines for performing statistical analyses of data, and least squares and numerical curve fitting methods for analyzing experimental data, along with numerical methods for solving ordinary and partial differential equations. The final chapter offers optimization methods for the minimization or maximization of functions. Exploiting the useful features of C#, this book shows how to write efficient, mathematically intense object-oriented computer programs. The vast array of practical examples presented can be easily customized and implemented to solve complex engineering and scientific problems typically found in real-world computer applications.

The paper describes a Coalition Project for the reform of engineering education in the state of Santa Catarina, in the southern part of Brazil. New teaching/learning methodologies are conceived for the academic formation of a professional tuned up to the technological dynamic of his/her time and to the challenges to the engineering profession anticipated for the coming century. The approaches described are the backbone of a project for the restructuring of engineering education, led by the Federal University of Santa Catarina. The project unfolds over three major actions. The first is connected with the election of engineering as a career. A methodology for the search of talents is proposed; it is based upon the Synthesis of Multiple Intelligence and is meant to be taken to high school students as a motivating and probing contact with the challenges of the engineering profession. The second action, that complements the first, involves the early exposure of engineering students to engineering themes and problems during the first part of the course. The study of Mathematics, Physics, Chemistry, etc. shall be coupled to an initiation at engineering problems and methods. This kind of approach and its methodology should facilitate the insertion of the students into the context of engineering problems from the beginning of his/her academic trajectory. Finally, the last action should be developed at the level of the applied courses.

The newly generated cities inside Egypt are in greet need for the assessment of engineering problems and natural hazards. New Cairo City is one of the biggest urban areas that have huge amount of investments now. Seismic hazard assessment is used to identifying the amount of shaking that may reach New Cairo City area and the new construction may suffer from. A modified and updated earthquake catalogue till 2003, for earthquakes occurring in Egypt and surrounding areas is used for estimation of recurrence relationships and regression constants. Maximum magnitude earthquake was calculated for 72 source zones used in the present study to evaluate the amount of risk at the New Cairo city area. These data were used to generate Peak Ground Acceleration (PGA) contour maps based on the regionally developed PGA attenuation relations for all shallow seismic sources for respective forecast time periods (exposure times) 25 and 50 years. Hazard maps were calculated using the computer program developed by McGuire. One of the biggest engineering problems that constitutes a potential hazard is the clay and marl intercalations exist in the area. The clay is considered as a dangerous unwanted layer in some formations because of its engineering problems and unrealistic amount of swilling especially in the area of study. To detect and trace this unwanted layer a total of 23 seismic refraction profiles are conducted using three shots for each profile. GRM is used to interpret the acquired data, the resulted depth sections are verified by advanced Finite Difference (FD) technique. Moreover samples were taken as possible from this clays to investigate its swelling. A final map for best safe locations from geophysical point of view is constructed.

Demand for lightweight, efficient, and low cost structures seems mandatory because of growing realization of the rarity of raw materials and rapid depletion of convention energy sources. This requires engineers to be aware of optimization techniques. Designing, analyzing, and solving civil engineering problems can be very large scale and can be highly nonlinear, and to find solutions to these problems is often very challenging. In the past two decades, soft computing methods are becoming an important class of efficient tools for developing intelligent systems and providing solutions to complicated engineering problems. The papers selected for this special issue represent a good panel in recent challenges. The topics of these papers are connected with the computational intelligence methods and their application in civil and hydraulic engineering. An investigation on different metaheuristics abilities for engineering problems was studied by O. Adekanmbi and P. Green. They utilized the third version of generalized differential evolution (GDE) for solving practical engineering problems. GDE3 metaheuristic modifies the selection process of the basic differential evolution and extends DE/rand/1/bin strategy. Performance-based seismic design of steel frames using the colliding bodies optimization (CBO) algorithm as new optimization method was presented by H. Veladi. A pushover analysis method based on semirigid connection concept was developed and the CBO algorithm is employed to find optimum seismic design of frame structures. H. Veladi solved two numerical examples from literature and show the power or weakness of this new algorithm. A parametric study of nonlinear seismic response analysis of transmission line structures and the effect analysis of strain rate on power transmission tower-line system under seismic excitation were developed by L. Tian et al. in two papers. In one of them, nonuniform ground motions are generated using a stochastic approach based on random vibration analysis. Then, the effects of multicomponent ground motions, correlations among multicomponent ground motions, wave travel, coherency loss, and local site on the responses of the cables were investigated using nonlinear time history analysis method. The results showed the multicomponent seismic excitations should be considered, but the correlations among multicomponent ground motions could be neglected. While, in the other, a three-dimensional finite element model of a transmission tower-line system was created based on a real project. The results showed that the effect of strain rate on the transmission tower generally decreases the maximum top displacements, but it would increase the maximum base shear forces, and thus it is necessary to consider the effect of strain rate on the seismic analysis of the transmission tower. The effect of strain rate could be ignored for the seismic analysis of the conductors and ground lines, but the responses of the ground lines considering strain rate effect are larger than those of the conductors. A study of bridge structures is performed by N. Easazadeh Far and M. Barghian. They selected integral abutment bridges (IABs) as jointless bridges. Although all developed bridge design codes consider temperature and earthquake loads separately in their specified load combinations for conventional bridges with expansion joints, the thermal load is an “always on” load and during the occurrence of an earthquake, these two important loads act on bridge simultaneously. Safety identifying of these bridges under seismic and thermal loads is the main aim of their work where the safety of IABs, designed by AASHTO LRFD bridge design code, under combination of thermal and seismic loads was studied. They showed that for an IAB designed by AASHTO LRFD the reliability indexes have been reduced under combined effects. In the field of hydraulic engineering, optimal design of pipe sizes for looped irrigation water supply system is presented by D. G. Yoo et al. in which they developed a harmony search algorithm to fulfill this aim. Their study mainly serves two purposes. The first is to develop an algorithm and a program for estimating a cost-effective pipe diameter for agricultural irrigation water supply systems using optimization techniques. The second is to validate the developed program by applying the proposed optimized cost-effective pipe diameter to an actual study region (Saemangeum project area, zone 6). They show that the optimal design program can be effectively applied for the real systems of a looped agricultural irrigation water supply.

May 15-19, 2022 Francavilla al Mare (Chieti), ITALY Introduction This Proceedings of the Journal of Physics: Conference Series contains a subset of papers presented at the 10th International Conference on Inverse Problems in Engineering (ICIPE), hosted by the Department of Industrial and Information Engineering and Economics, University of L’Aquila, Italy, and held in Francavilla al Mare (Chieti), May 15 – 19, 2022.Due to Coronavirus emergency and to protect the health and safety to all our participants, the 10th Edition, scheduled during May 18-21, 2020, and then May 16-20, 2021, was postponed to May 15-19, 2022, and termed as ICIPE 22.Since the first ICIPE in 1993, this conference has served as the main international venue for collaboration and interaction between applied mathematicians who develop inverse analysis tools, and engineers who use these tools in many different disciplines of science such as manufacturing and machining processes, medical imaging, oil exploration, radar, sonar and seismology, space applications, non-destructive testing and so on. The 2022 meeting continued this tradition, with more than 50 delegates from many sub-disciplines of engineering, science, and applied mathematics. The number of participants was lower than the standard number of 80 – 120 due to both covid travel restrictions in some Asian and American countries and conflict in Ukraine.List of Dedication, References, Organizing Committee, Local Committee, Scientific Committee, List of Registrants, Sponsors and Logos are available in this pdf.

Multi-scale problems in engineering often require modeling approaches that effectively integrate phenomena occurring across different spatial and temporal scales. Hybrid modeling approaches provide a promising solution by combining the strengths of numerical and analytical methods from various scales to enhance both accuracy and computational efficiency. This article reviews a range of hybrid techniques for addressing multi-scale challenges, including the integration of micro- and macro-scale models, coupling discrete and continuum simulations, and the application of multilevel methods in engineering analysis. Case studies from diverse engineering disciplines are presented to illustrate the potential benefits and challenges of hybrid modeling approaches. Leveraging these methods aims to deliver more realistic engineering solutions while optimizing computational resources.

The genetic algorithm BIANCA, developed for design and optimisation of composite laminates, is a multi-population genetic algorithm, capable to deal with unconstrained and constrained hard combinatorial optimisation problems in engineering. The effectiveness and robustness of BIANCA rely on the great generality and richness in the representation of the information, i.e. the structure of populations and individuals in BIANCA, and on the way the information is extensively exploited during genetic operations. Moreover, we developed proper and original strategies to treat constrained optimisation problems through the generalisation of penalisation methods. BIANCA can also treat constrained multi-objective problems based on the construction of the Pareto frontier. Therefore, BIANCA allows us to approach very general design problems for composite laminates, but also to make a step forward to the treatment of more general problems of optimisation of materials and structures. In this paper, we describe specifically the case of optimal design of composite laminates, concerning both the theoretical formulation and the numeric resolution.

We present some developments in the formulation of the Particle Finite Element Method (PFEM) for analysis of complex coupled problems on fluid and solid mechanics in engineering accounting for fluid-structure interaction and coupled thermal effects, material degradation and surface wear. The PFEM uses an updated Lagrangian description to model the motion of nodes (particles) in both the fluid and the structure domains. Nodes are viewed as material points which can freely move and even separate from the main analysis domain representing, for instance, the effect of water drops. A mesh connects the nodes defining the discretized domain where the governing equations are solved, as in the standard FEM. The necessary stabilization for dealing with the incompressibility of the fluid is introduced via the finite calculus (FIC) method. An incremental iterative scheme for the solution of the non linear transient coupled fluid-structure problem is described. The procedure for modelling frictional contact conditions at fluid-solid and solidsolid interfaces via mesh generation are described. A simple algorithm to treat soil erosion in fluid beds is presented. An straight forward extension of the PFEM to model excavation processes and wear of rock cutting tools is described. Examples of application of the PFEM to solve a wide number of coupled problems in engineering such as the effect of large waves on breakwaters and bridges, the large motions of floating and submerged bodies, bed erosion in open channel flows, the wear of rock cutting tools during excavation and tunneling and the melting, dripping and burning of polymers in fire situations are presented.

T. Wichtmann, T. Triantafyllidis: Behaviour of granular soils under environmentally induced cyclic loads. - D. Muir Wood: Constitutive modelling. - C. di Prisco: Creep versus transient loading effects in geotechnical problems. - M. Pastor et al.: Mathematical models for transient, dynamic and cyclic problems in geotechnical engineering. - M. Pastor: Discretization techniques for transient, dynamics and cyclic problems in geotechnical engineering: first order hyperbolic partial diffential equations. - M. Pastor et l.: Discretization techniques for transient, dynamic and cyclic problems in geotechnical engineering: second order equation. - C. di Prisco: Cyclic mechanical response of rigid bodies interacting with sand strata. - D. Muir Wood: Macroelement modelling. - M. F. Randolph: Offshore design approaches and model tests for sub-failure cyclic loading of foundations. - M.F. Randolph: Cyclic interface shearing in sand and cemented solis and application to axial response of piles. - M. F. Randolph: Evaluation of the remoulded shear strength of offshore clays and application to pipline-soil and riser-soil interaction.

Constrained optimization problems in mechanical engineering are very difficult for the optimization algorithm. In 2013, an improved version of constrained differential evolution, named ArATM-ICDE was proposed to optimize the constrained optimization problem. An archiving-based adaptive trade-off model (ArATM) was constructed to handle the constraints; resulting in an algorithm referred to as ArATM-ICDE. This paper applies ArATM-ICDE to solve constraint optimization problems in mechanical engineering. We also combine the penalty technique for constraint handling into the ICDE, named Penalty-ICDE; which compares the abilities of the constraint handling techniques. Our experiments were conducted on ten widely used constraint engineering optimization problems. The experiment results proved the ArATM-ICDE to be more reliable than the Penalty-ICDE. Additionally, ArATM-ICDE consumed a lesser number of function calls than Penalty-ICDE. This paper further compared the effectiveness of ArATM-ICDE and Penalty-ICDE with eight state-of-the-art algorithms, which revealed that ArATM-ICDE and Penalty-ICDE produced solutions of higher quality than those produced by the comparative algorithms. The ArATM-ICDE also consumed less effort in its process.

Special Issue on UHV air insulation: Physical and Engineering Research

This paper develops a metaheuristic, the Natural Selection Optimization Algorithm (NSOA), taking inspiration from the natural selection and the survival, growth, and reproduction of the fittest. The algorithm uses two instruments: Normal distribution and Sigmoid function. The Normal distribution generates random numbers such that the individuals in the initial population obey a Normal distribution, which can place search agents appropriately. The Sigmoid function controls the search process of the NSOA, aiding the convergence of the algorithm. To appreciate the global search ability of the NSOA, we test the NSOA against 52 benchmark functions, a hydrogeologic parameter estimation problem, and three engineering problems. Moreover, this paper compares the NSOA with six other algorithms under the same experimental configuration. Our results show that, for most functions, the NSOA converges and extracts the optimal value faster than the other established algorithms, pointing to the novelty and practical efficacy of the NSOA.