Applied Problems Of Mechanics Research Articles

Applied Mechanics Problems Accompanying Spacecraft Launches from a Floating Platform and Their Resolution by the Sea Launch Project

The technologies applied by SDO Yuzhnoye to implement the Sea Launch Project are exemplified to describe the recent achievements in designing space launch vehicles. Consideration is given to the loads acting on launch vehicles during long-term sea transportation and prelaunch operations in rough sea. Experimental methods for determining those loads are described, and techniques for reducing them are proposed. Presentation is also given to methods of providing launch safety under conditions of limited space for launch-support equipment and reducing the thermal and vibroacoustic loads on the launcher. The efficiency of the methods described is confirmed by the success of the Sea Launch Project

Coincidence of Boobnov-Galerkin and Closed-Form Solutions in an Applied Mechanics Problem

It is shown that the utilization of the Filonenko-Borodich set of functions, as the comparison functions in the Boobnov-Galerkin method leads to the result that coincides with the closed-form solution for the clamped-clamped uniform beam under uniformly distributed load. It is hoped that this remarkable, direct coincidence could be used in graduate courses and books on mechanics of solids.

Contrasting probabilistic and anti-optimization approaches in an applied mechanics problem

Probabilistic and non-probabilistic, anti-optimization analyses of uncertainty are contrasted in this study. Specifically, the comparison of these two competing approaches is conducted for an uniform column, with initial geometric imperfection, subjected to an impact axial load. The reliability of the column is derived for the cases when the initial imperfections posses either (a) uniform probability density, (b) truncated exponential density or (c) generic truncated probability density. The problem is also analyzed in the context of an interval analysis. It is shown that in, the most important near-unity reliability range these two approaches tend to each other. Since the interval analysis constitutes a much simpler procedure than the probabilistic approach, it is argued that the former is advantageous over the latter in some circumstances.

Anti-Optimization Versus Probability in an Applied Mechanics Problem: Vector Uncertainty

In this study probabilistic and nonprobabilistic anti-optimization approaches are contrasted to evaluate their relative advantages and disadvantages while solving a mechanical problem in presence of vector uncertainty. The different cases that are analyzed in probabilistic setting that deal with either uniform or generic probability density functions for the uncertain variables varying in a rectangular domain. This case has been compared with interval analysis, a particular case of anti-optimization. The presence of a convex, smooth boundary of the uncertain domain has been also considered for comparing results obtained with these two alternative methods. It is shown that in case of vector uncertainty the anti-optimization method yields the same solution for the design problem as is provided by means of more complex probabilistic considerations. [S0021-8936(00)03103-2]

The First Scientific-Engineering Symposium “Contemporary Problems of Engineering Mechanics”

The symposium was held according to a proposal of the Board of the Ukrainian Society on Fracture Mechanics of Materials and the administration of the Lutsk State Technical University. At present, along with the traditional approaches, engineering mechanics uses the achievements of the mechanics of deformable solids, fracture physics, and materials science. The systematic elucidation of fundamental and applied results at international forums demonstrates the importance of these investigations and the high authority of Ukrainian scientists. The State Western Scientific Center of the Ukrainian Academy of Sciences, in particular, the Karpenko Physicomechanical Institute and the Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, the Institute of Strength Problems, the Paton Institute of Electric Welding, the Franko L’viv National University, the State University “L’vivs’ka Politekhnika,” the Lutsk State Technical University, and other Ukrainian scientific and educational institutions continue to fruitfully work on the solution of urgent problems of the mechanics of deformation and fracture of materials and on the introduction of the achievements of mechanics into the development of technologies and design in building and machine building. The aim of this symposium was to generalize the most important results in this field of knowledge, to stimulate the solution of specific problems arising in the course of the development of modern technologies and designing methods, to bring scientific investigations nearer to engineering practice, in particular, concerning the determination of the residual resource of engineering structures of long-term service, to acquaint the general scientific-engineering community and students with the results of scientific research, and to study the possibilities of commercializing investigations and developing international collaboration.

Quantifier elimination in applied mechanics problems with cylindrical algebraic decomposition

The method of cylindrical algebraic decomposition (CAD) of the k-dimensional space constitutes a classical technique for the efficient solution of quantifier elimination (QE) problems in algorithmic, computer-aided algebra. Here we apply this method to some applied mechanics problems under appropriate constraints. At first, we study the problem of a straight elastic beam under a restriction on the maximum permissible deflection along this beam (which can easily be reduced to the construction of a one-dimensional CAD) as well as the problem of a circular isotropic elastic medium where a stress component should not exceed a critical value (which requires the construction of a three-dimensional CAD). In both these problems, we derive also the required quantifier-free formulae (QFFs) not including the fundamental variables, but only the parameters involved. Much more difficult CAD/QFF-derivation applications, concerning an elliptical elastic medium again with an upper bound for a stress component, a special case of failure by yielding in fracture mechanics, related to Sih's strain-energy-density factor, and a frictionless contact problem for an elastic half-plane are also considered and explicitly solved with the help of already available CAD-produced results although, evidently, CAD is not expected to produce QFFs in extremely difficult problems. ,Finally, additional possible applications of CAD/CQE to applied mechanics problems are also suggested.

Applied Problems of Mechanics of Composite Structures

The mechanics of composites as an independent branch of the mechanics of deformable media is in the stage of growth, development and formation. Its branches have been expanded to various extents; many problems are far from completion, yet the advances in engineering mechanics of composites are indisputable. These advances are connected with the solution of applied problems in the most advanced industries. The first stage of the development of the mechanics of composite structures, mainly intuitive, has been completed. It is appropriate to give preliminary resume and consider further directions of investigations. In this regard it is of great interest to consider experience of the scientists of former USSR having made considerable contribution to the mechanics of composite structures. The present review is based on the examples belonging to the scope of interest of the authors and, naturally, does not claim to exhaust the theme.

Inequality constraints in rectangular finite/boundary elements

During the practical application of the finite element and boundary element methods to applied mechanics problems, we frequently encounter situations where a quantity of interest in such an element should satisfy an inequality inside the whole element. Here we consider the case of a simple two-dimensional rectangular element with eight nodes and we derive a quantifier-free formula (independent both of the universal quantifier and of the Cartesian coordinates) for the positivity of the fundamental quantity in this element on the basis of recent quantifier elimination results by Collins for the cubic univariate polynomial. The derived formula shows exactly for which numerical values of the fundamental quantity at the nodes of the element we must be sure about the satisfaction of the inequality involved (positivity) inside the whole element. Several applied mechanics problems, such as contact and crack problems in the boundary element method and problems concerning maximum permissible values for the displacement, stress and strain components in the finite element method, can be studied by the present approach. Several possible future generalizations are also suggested in brief and an alternative possibility, based on Sturm-Habicht sequences for polynomials, is studied in some detail both for the quadratic and for the cubic polynomial.

Optimization of variational methods

Lord Rayleigh proposed his now classical method (based on a one-term deflection function) in 1870. On the other hand, he suggested in 1894 the possibility of optimizing the eigenvalues (natural frequencies or buckling loads) by minimizing them with respect to an exponential parameter contained in the coordinate function. This optimization approach has become increasingly popular in the last decade and it has been extended to other variational methods and bounding techniques. The present paper reviews recent developments in this area which consists, essentially, in a nonlinear optimization process of the coordinate functions in a global sense. The technique is applicable in a large variety of applied mechanics problems of considerable interest to ocean engineers dealing with the analysis of mechanical systems.

Symbolic computations for the solution of inverse/design problems with Maple

Symbolic computations during the solution of applied mechanics problems permit the derivation of results of general validity with respect to the parameter(s) used. Here this approach is generalized to the cases when, beyond possible linear equations, nonlinear polynomial equations appear also in the exact/approximate methods used. The cases of three elementary inverse/design torsion problems in classical isotropic elasticity, where the dimensions of the cross-section of the bar should be determined if the torque and the maximum shear stress are known in advance, are used for the illustration of the method, which leads to a polynomial equation with respect to the fundamental unknown variable. The computer algebra system Maple V and the Gröbner bases method are used for the derivation of the present results. Finally, several serious factors influencing the computations in the present method, which generally requires a large amount of symbolic computations, are considered in some detail.

A non‐Jacobian numerical quadrature for semi‐infinite integrals

AbstractA non‐Jacobian numerical quadrature is proposed for evaluating improper integrals over a semi‐infinite range. The quadrature first transforms the semi‐infinite integration limit into a finite limit between – 1 and 1. Standard numerical integration procedures such as Gauss–Chebyshev or Gauss–Legendre schemes can then be used to obtain the integral value. Unlike traditional methods using Laguerre or Hermite polynomials, numerical results show that no specific weight function is required for the proposed quadrature to converge as long as the integral exists. The transformation also includes a scale parameter which effectively expands the numerical‐integration sampling points along its original semi‐infinite integration path. Numerical examples shows that selection of the scale parameter is rather flexible and convergence can always be achieved within a wide range of parameter values. Several applied mechanics problems are also illustrated to validate the proposed numerical scheme. The quadrature can be easily incorporated into finite element or boundary element schemes for the evaluation of semi‐infinite integrals.

Subdifferential and variational formulations of boundary value problems

A natural constructive method for variational formulations of constrained nonlinear boundary value problems is presented. The method consists in dualizing convex conditions and constraints via the inverse graph of corresponding local subdifferential formulations. No assumption of potentiality is required. The method is tested by obtaining variational formulations of typical applied mechanics problems, which in general correspond to coupled systems of variational inequalities and give a basis for constructing numerical schemes.

The Use of Projectors in Some Problems of Applied Mechanics and Optics

AbstractThe use of projectors and their derivatives is illustrated in the cases of geometry on hypersurfaces, the deformation of thin shells and the modification in holography.

Special Issue on Applied Mechanics Problems in Industry: Introduction

Special Issue on Applied Mechanics Problems in Industry: Introduction

Applied Mechanics Problems in the Oil and Gas Industry

The petroleum industry offers a broad spectrum of problems that falls within the domain of expertise of mechanical engineers. These problems range from the design of well production equipment to the evaluation of formation responses to production and stimulation. This paper briefly describes various aspects and related difficulties with which the oil industry has to deal, from the time the well is spudded until the field is abandoned. It attempts to delineate the problems, to outline the approaches presently used, and to discuss areas where additional research is needed. Areas of current research activity also are described; whenever appropriate, typical or pertinent case histories are used to illustrate a point.

Applied Mechanics Problems in Automotive Engineering

The automotive industry is undergoing a technological revolution unparalleled since its infancy. Increased foreign competition, particularly in terms of product cost, has created a need for technological innovation both in automotive products and in automotive manufacturing and assembly processes. Applied mechanics research has become a critical element in many of the areas which can promote improved products and process efficiency. Several major research programs which are underway at General Motors will be reviewed and used to motivate the discussion of important applied mechanics problems. Research examples will include automated vehicle design technology, advanced materials, and mechanics of manufacturing processes. Suggested research spans the entire range of the applied mechanics field, from basic theory to numerical applications. Experimental research is as vital to further progress as is analytical research. Considerably more emphasis should be given to relating mechanical performance of the finished product to its fabrication.

On the Ergodicity Assumption in an Applied Mechanics Problem

A deformation of a thin uniform cylindrical shell is considered under random axisymmetric loading. Mathematically this is equivalent to the study of a quasi-linear differential equation with random inhomogeneous term and random coefficient. The approximate method of solution, based on the assumption of ergodicity of the shell slope, is first described. It is shown that sometimes this assumption is valid but when not, it may yield non-negligible errors. In particular, it is shown via the exact solution that assumption of ergodicity of the shell slope is correct if the loading is ergodic in correlation. However, this assumption may yield an error of about 20 percent if the loading in ergodic in mean-square but not in correlation.

A drafting program for isoparametric finite elements

AbstractConsiderable effort has been invested lately in the application of isoparametric finite elements for numerical solution of a wide range of applied mechanics problems. In fact, several general purpose computer programs are now available which are based upon such finite elements. In the present paper, a new application of the isoparametric finite element concept is introduced which significantly extends its usefulness for many practical structural configurations. In this application, final working or architectural drawings of the structure are made from the same (or similar) finite element model as was utilized in a structural integrity analysis. The hardware necessary to produce such drawing, a computer driven plotter or automated drafting machine, is available commercially or through most data centres, and the software concepts required are described herein.

A critical look at the design of reinforced concrete for ductility

In designing adequate ductility into a frame structure to resist earthquake forces, the portion of the procedure which has the least satisfactory theoretical and experimental basis is the strictly design part. This is the section in which the designer, having assessed the ductility demands of the various members of the frame, proceeds to decide on the concrete dimensions and reinforcement pattern which will satisfy these demands. The reasons for the shortcomings are fairly obvious. Unlike frame analysis and frame response, which can be dealt with as tidy applied mechanics problems, investigation of the design problems requires research workers with an extensive design background, and an awareness of all the design criteria which have to be satisfied. Unfortunately, such research workers are rare, and consequently insufficient research has been carried out. What research has been done has obviously not been planned with a view to obtaining information that can be used in design.

Russian Papers on Pure and Applied Mathematics

AMONG Russian periodicals and books recently received are several containing papers on pure and applied mathematics. A striking feature is the many investigations of elasticity problems in Applied Mathematics and Mechanics. There are also many other papers of considerable interest, for example, the paper on the flow of a gas at supersonic velocities by V. S. Tatarenchik (App. Maths. and Mechanics, 8, 401; 1943), which should be compared with current investigations by Southwell and his colleagues (Nature, 154, 90 and 834; 1944). N. N. Parijsky gives (Astron. J. S. U., 21, 78; 1944) the result of calculations which support Russell's criticism of Jeans' theory of the origin of the solar system. In addition to the journals mentioned above, we have also received a valuable atlas of nomograms, containing thirty-seven plates. All the publications received are being deposited in the Science Museum, South Kensington, London, S.W.7, where they will be available for anyone who desires to consult them. By the aid of the summaries in English or French, it should be fairly easy for those entirely ignorant of Russian to understand the results and methods of the papers.