Structural Imposed Load Analysis of Isotropic Rectangular Plate Carrying a Uniformly Distributed Load Using Refined Shear Plate Theory

This presents the static flexural analysis of a three edge simply supported, one support free (SSFS) rectangular plate under uniformly distributed load using a refined shear deformation plate theory. The shear deformation profile used, is in the form of third order. The governing equations were determined by the method of energy variational calculus, to obtain the deflection and shear deformation along the direction of x and y axis. From the formulated expression, the formulars for determination of the critical lateral imposed load of the plate before deflection reaches the specified maximum specified limit and its corresponding critical lateral imposed load before plate reaches an elastic yield stress is established. The study showed that the critical lateral imposed load decreased as the plates span increases, the critical lateral imposed load increased as the plate thickness increases, as the specified thickness of the plate increased, the value of critical lateral imposed load increased and increase in the value of the allowable deflection value required for the analysis of the plate reduced the chances of failure of a structural member. This approach overcomes the challenges of the conventional practice in the structural analysis and design which involves checking of deflection and shear after design; the process which is proved unreliable and time consuming. It is concluded that the values of critical lateral load obtained by this theory achieve accepted transverse shear stress to the depth of the plate variation in predicting the flexural characteristics for an isotropic rectangular SSFS plate. Numerical comparison was conducted to verify and demonstrate the efficiency of the present theory, and they agreed with previous studies. This proved that the present theory is reliable for the analysis of a rectangular plate. Keywords— Allowable deflection, critical imposed load, energy method, plate theories, shear deformation, SSFS rectangular plate

Nonlinear Deformation and Numerical Post-Buckling Analysis of Plate Structures Using the Assumed Natural Strain Concept

In this study, an efficient triangular element for the fast nonlinear analysis of moderately thick Mindlin–Reissner plates is proposed. The element is formulated using a newly developed method, which is based on the assumed natural strain concept, and called Continuously Variable Strain (CVS). The continuous higher-order strain field is proposed by using the fundamental lemma of the variational calculus. Furthermore, the updated Lagrangian tensor together with rigid body terms is employed allowing for large deformations. The proposed element (CVST10), which is obtained by minimizing the total potential energy, has only 10 degrees of freedom and demonstrates high-efficiency and fast convergence rate in analysis of problems with coarse and distorted meshes. The arc-length iterative technique is applied to handle the geometrically post-buckling behavior of homogeneous plates under various load and boundary conditions. Various numerical examples prove the accuracy of the proposed element.

IMPLEMENTATION OF THE ADVANCED LEARNING IN THE PROCESS OF FUNDAMENTAL MATHEMATICAL TRAINING OF BACHELORS IN THE FIELD OF ELECTRONICS AND TELECOMMUNICATION

The article substantiates the expediency of the implementation of the advanced learning in the process of fundamental mathematical training of bachelors in the field of electronics and telecommunications. At the moment, the field requires mandatory (deep) knowledge of the main classical sections of mathematics, it is also important to acquaint students in higher mathematics with elements of modern mathematical theories, concepts that allow learners to better understand special courses in mathematics and relevant special disciplines. materials of mathematics, which are used in the modern mathematical models of technical developments. The aim of the article is to reveal the approaches to the concept of the advanced learning in the process of fundamental mathematical training of future bachelors in the field of electronics and telecommunications.The main methods that were implemented in the study of the problem of advanced learning were the analysis and synthesis of the scientific sources on the selected problem, observation, implementation of projects and evaluation of their results. It is offered (from the first semester) to introduce generalized concepts (norm, operator, etc.) in time, to acquaint with ideas of variational calculus, functional analysis, mathematical methods of research of linear equations with variable coefficients, theory of stochastic approximation, mathematical modelling. Then the future specialist will be able to comprehend the objects, which have been already developed by mathematicians but have not been used yet. Thus, a difficult topic or concept can be considered in advance in some connection with the currently studied material. For example, during the study of a function and the construction of its graph, along with the asymptote, students can be introduced to the approximation of the function, the concepts of interpolation and approximation. It is expedient to acquaint students with these problems more deeply during performance of independent tasks (consultations, the abstract, the report at conference, etc.).

An analytical and probabilistic model with concordance for detecting mine-like objects with mirror symmetry

PurposeThe purpose is to develop search and detection strategies that maximize the probability of detection of mine-like objects.Design/methodology/approachThe author have developed a methodology that incorporates variational calculus, number theory and algebra to derive a globally optimal strategy that maximizes the expected probability of detection.FindingsThe author found a set of look angles that globally maximize the probability of detection for a general class of mirror symmetric targets.Research limitations/implicationsThe optimal strategies only maximize the probability of detection and not the probability of identification.Practical implicationsIn the context of a search and detection operation, there is only a limited time to find the target before life is lost; hence, improving the chance of detection will in real terms be translated into the difference between success or failure, life or death. This rich field of study can be applied to mine countermeasure operations to make sure that the areas of operations are free of mines so that naval operations can be conducted safely.Originality/valueThere are two novel elements in this paper. First, the author determine the set of globally optimal look angles that maximize the probability of detection. Second, the author introduce the phenomenon of concordance between sensor images.

Optimizing Regenerative Braking: A Variational Calculus Approach

We begin by analyzing, using basic physics considerations, under what conditions it becomes energetically favorable to use aggressive regenerative braking to reach a lower speed over “coasting” where one relies solely on air drag to slow down. We then proceed to reformulate the question as an optimization problem to find the velocity profile that maximizes battery charge. Making a simplifying assumption on battery-charging efficiency, we express the recovered energy as an integral quantity, and we solve the associated Euler–Lagrange equation to find the optimal braking curves that maximize this quantity in the framework of variational calculus. Using Lagrange multipliers, we also explore the effect of adding a fixed-displacement constraint.

APPLICATION OF THE ”WAVE“ METHOD TO SOLVE THE PROBLEMS OF OPTIMIZATION OF PASSENGER AND CARGO TRANSPORTATION IN MEGACITIES TO IMPROVE THEIR TRANSPORT NETWORK AND INFRASTRUCTURE. Conceptual basis, mathematical framework

The paper proposes a new approach to solving optimization problems arising in engineering and transport logistics in designing and construction of roads (in particular, in megacities, near large transport hubs, near state borders) for cargo and passenger transportation and implementation of international trade. The fundamental problems of modern engineering logistics - the problem of optimal location (transport hubs) and the problem of identification and segmentation of logistics, transport and logistics zones are considered. These problems are solved using methods of variational calculus, in particular, the so-called "wave" method based on the Fermat principle existing in physical optics, which is based on the analogy between finding the global extremum of the integral functional and the propagation of light in an optically heterogeneous medium. A numerical method for the above technique has been developed programatically. The idea of the "wave method/approach belongs to V.V. Bashurov, who proposed to use the methods of geometrical and physical optics to investigate applied safety problems and some related issues. The essence of the "wave method" is that initially the safety problem is reduced to the search for the global minimum of a nonlinear functional. In turn, the minimization problem is solved by constructing the trajectory of motion of the front of the "light wave" moving in an optically inhomogeneous medium. Finding the minimum of a functional is a classical problem of variational calculus, for the solution of which a significant mathematical apparatus has been developed. However, most of known methods effectively determine only local extrema. "Wave" method allows to solve the problem of finding a global extremum with greater efficiency. This paper proposes a conceptual framework and scientifically justified modification of this "wave" method for solving optimization problems arising in engineering and transport logistics, including the problem of optimal location of the transport hub, transport and logistics center (warehouse) and the problem of optimal identification and segmentation of logistical zones (metropolitan areas, large transport hubs).