Michael J. Cloud's research while affiliated with Lawrence Technological University and other places

Publications (66)

Article
A study of existence and uniqueness of weak solutions to boundary value problems describing an elastic body with weakly nonlocal surface elasticity is presented. The chosen model incorporates the surface strain energy as a quadratic function of the surface strain tensor and the surface deformation gradients up to Nth order. The virtual work princip...
Article
Full-text available
Within the framework of the nonlinear elastic theory of micromorphic continua we derive the conditions for propagation of acceleration waves. An acceleration wave, also called a wave of weak discontinuity of order two, can be treated as a propagating nonmaterial surface across which the second derivatives of the placement vector and micro-distortio...
Book
Engineers are smart people. Their work is important, which is why engineering material should be written as deliberately and carefully as it will be read. Engineering Writing by Design: Creating Formal Documents of Lasting Value demonstrates how effective writing can be achieved through engineering-based thinking. Based on the authors' combined exp...
Article
Full-text available
Courants minimax variational principle is considered in application to the six-parameter theory of prestressed shells. The equations of a prestressed micropolar shell are deduced in detail. Courants principle is used to study the dependence of the least and higher eigenfrequencies on shell parameters and boundary conditions. Cases involving boundar...
Article
The purpose of this paper is to use a weak setup to justify application of the finite element method (FEM) to the equilibrium problem for a nonlinear model of a shallow shell clamped along part of an edge constrained by a frictionless obstacle. A suitable energy space is constructed and the generalized (weak) solutions are introduced. The obstacle...
Chapter
Some major advances in mathematics have occurred through the extension of existing number systems. The natural numbers were extended to the real numbers, the real numbers to the complex numbers, and so on.
Chapter
Inequalities lie at the heart of mathematical analysis. They appear in the definitions of continuity and limit (and hence in the definitions of the integral and the derivative). They play crucial roles in generalizing the notions of distance and vector magnitude. But many problems of physical interest also rely on simple inequality concepts for the...
Chapter
In this chapter we revisit some facts from mathematical analysis and show how these may be used to establish important inequalities. We begin by reviewing convergence of real number sequences and continuity of real functions of a single variable.
Chapter
Here we examine certain famous inequalities that have left bold imprints on both pure and applied mathematics. These results, some of which are very old, pertain to functions, sequences, and integrals. We recall that integral inequalities are frequently deduced by establishing the corresponding result for series, writing it out for Riemann sums, an...
Chapter
In the theory of differential equations, inequalities are widely used to estimate or approximate solutions to problems. They are also needed to establish uniqueness and existence, along with other theoretical results pertaining to solution behavior. The purpose of this chapter is to touch on a few inequalities that play key roles in the study of di...
Chapter
Generality is gained by working in abstract spaces. For instance, all essential aspects of the topics of convergence and continuity can be studied in the context of a metric space. When we search for solutions to problems of physical interest, we must often search among the members of linear spaces (also known as vector spaces). Inequalities provid...
Chapter
The reader who has worked patiently through the mathematical content of the previous chapters should be comfortable dealing with the applications treated here. These topics were chosen for variety and are presented in no particular order (just as we might encounter them in practice).
Chapter
From a functional analytic standpoint, nonlinear problems of mechanics are more complicated than linear problems; as in mechanics, they require new approaches. Many, like the problems of nonlinear elasticity in the general case, provide a wide field of investigation for mathematicians (see Antman [2]); the problem of existence of solutions in nonli...
Chapter
In the past, an engineer could calculate mechanical stresses and strains using a pencil and a logarithmic slide rule. Modern mechanical models, on the other hand, are nonlinear, and even the linear models are complicated. Numerical methods in structural dynamics cannot be applied without computers running specialized programs. However, a researcher...
Chapter
Consider a set of particles P 1, …, P n. To locate these particles in the space ℝ3, we need a reference system. Let the Cartesian coordinates of particle P i be (ξi, ηi , ζi ). Identifying (ξ1, η1, ξ1) with the triple (x1, x2, x 3), (ξ2, η2, ζ2) with (x,4, x,5, x,6), and so on, we obtain a vector x of the Euclidean space ℝ3n with coordinates (x1, x...
Book
Introduction.- Metric, Banach, and Hilbert Spaces.- Mechanics Problems from the Functional Analysis Viewpoint.- Some Spectral Problems of Mechanics.- Elements of Nonlinear Functional Analysis.- Summary of Inequalities and Imbeddings.- Hints for Selected Problems.- References.- In Memoriam: Iosif I. Vorovich.- Index.-
Chapter
We obtain a spectral problem by formally considering a solution u of the form
Article
Full-text available
A technique for automatic error analysis using interval mathematics is introduced. A comparison to standard error propagation methods shows that in cases involving complicated formulas, the interval approach gives comparable error estimates with much less effort. Several examples are considered, and numerical errors are computed using the INTLAB ex...
Book
Advanced Engineering Analysis is a textbook on modern engineering analysis, covering the calculus of variations, functional analysis, and control theory, as well as applications of these disciplines to mechanics. The book offers a brief and concise, yet complete explanation of essential theory and applications. It contains exercises with hints and...
Book
The tensorial nature of a quantity permits us to formulate transformation rules for its components under a change of basis. These rules are relatively simple and easily grasped by any engineering student familiar with matrix operators in linear algebra. More complex problems arise when one considers the tensor fields that describe continuum bodies....
Article
This book provides the general reader with an introduction to mathematical elasticity, by means of general concepts in classic mechanics, and models for elastic springs, strings, rods, beams and membranes. Functional analysis is also used to explore more general boundary value problems for three-dimensional elastic bodies, where the reader is provi...
Article
The natural frequencies of a hollow, perfectly conducting sphere with a circular aperture are calculated. The trajectories of the poles in the complex plane reveal an intriguing behavior which depends on whether the poles originate from internal or external sphere resonances. It is found that the modal degeneracy of the complete sphere is removed b...
Article
The transient backscattered field response of a ring above a lossy half space is investigated to gain a better understanding of the time-domain behavior of a radar target above the ocean or the earth's surface. The transition point from early to late time is determined for the three cases of the isolated ring, the ring above a lossless half space,...
Article
The natural resonant frequencies of an object embedded in a stratified conducting medium are considered. The special case of an annular ring is considered in detail. Extensive numerical results are examined for the case of a ring in free space above a conducting half space. This simple problem provides insight into the behavior of the natural frequ...
Article
A rigorous technique is presented for calculating the current induced on a thin lossy disk by rotationally symmetric sources, and the resulting scattered field. A Hallen-type integral equation is developed for the current using the magnetic vector potential, and it is solved by the method of moments. It is shown that the diffraction lobes usually a...
Article
Contenido: Cálculo básico de variaciones; Elementos de teoría del control óptima; Análisis Funcional; Algunas aplicaciones en mecánica.

Citations

... In general, incorporating surface stresses results in smoother solutions than in classic elasticity (see, for example, the analysis of weak solutions in Eremeyev & Lebedev, 2016;Eremeyev, Lebedev, & Cloud, 2021 ). Thus, one may expect a reduction of any singularities at the defect tip. ...
... Our focus on writing as a practice not a product and on rubrics as a shared articulation of learning goals and essential rhetorical moves allowed us to accommodate the broader shift from a deficit model to a contextual model (Gross, 1994;Perrault, n.d). It also allowed us to emphasize rhetoric as a critical component in science communication (Gross, 1994;Druschke and McGreavy, 2016) and the importance of a user-centered paradigm for designing effective communication artifacts (Rothwell and Cloud, 2017). ...
... Scholars worldwide have investigated ESL/EFL writing and many books and studies have been published on the topic [5][6][7]. The problems with ESL/EFL writing result from the absence of using the conventions and features of academic writing [8][9][10]. The texts are perceived to be vague and confusing, rhetorically unstructured, and overly personal. ...
... The aforementioned features have made the micromorphic and micropolar elasticity theories appropriate mathematical frameworks for studying the mechanics of materials with microstructure effects. So far, micromorphic and micropolar models have been utilized in different fields such as plasticity [15][16][17][18], granular materials [19], composite materials [20], piezoelectric materials [21,22], nanostructures [23][24][25], etc. [26][27][28][29][30]. Of course, the number of published papers on micromorphic models is less than that related to the micropolar models. ...
... Although this method is not commonly and presently evolving in soil mechanics and stabilization, it is the mission of this work to present the possibilities of utilizing this evolving mathematical method, which relies on the graphical behavior of a system to optimize its characteristic components. Fundamental approaches have been identified in the solutions of CoV, and they are known as Hamilton's and Brachistochrone problems [3,4]. While Hamilton's method is commonly used in solving most engineering problems, the Brachistochrone method handles systems with the effects of velocity, gravity, friction, and so on. ...
... At this stage, the curl and gradient of an arbitrary vector associated with the particle can be recast from Eq. (3) as [134] ...
... Information (data) forms information granules through information granulation. e representation forms of information granules often include interval [15], fuzzy set [16], and rough set [17]. e purpose of information granulation is to separate complex problems into several simpler problems. is way can make us capture the details of the problem. ...
... Consequently, the average value of f over [a,b] lies between m and M. [2] Similar to the above theorem, the next theorem gives a lower bound as well as an upper bound for linear functions under certain conditions. as well as defined at x=a and x=b with c, d ∈ Z + , the following inequality holds: ...
... This theory can be useful, for example, when modeling the initiation and growth of defects (holes, inclusions) [12,13], the growth of tissues [6,10,24], phase transformations [17], and wave propagation in prestressed solids [14]. In addition, this theory can be applied for the analysis of bodies with residual stresses at finite strains [1,2,5,7,19,24]. Analytical methods [4,11,13,15] and the finite element method (FEM) [14] are the main approaches to superimposed finite strains analysis. ...