John T. Katsikadelis

The boundary element method for nonlinear problems

In this paper a boundary-only boundary element method (BEM) is developed for solving nonlinear problems. The presented method is based on the analog equation method (AEM). According to this method the nonlinear governing equation is replaced by an equivalent nonhomogeneous linear one with known fundamental solution and under the same boundary conditions. The solution of the substitute equation is obtained as a sum of the homogeneous solution and a particular one of the nonhomogeneous. The nonhomogeneous term, which is an unknown fictitious domain source distribution, is approximated by a truncated series of radial base functions. Then, using BEM the field function and its derivatives involved in the governing equation are expressed in terms of the unknown series coefficients, which are established by collocating the equation at discrete points in the interior of the domain. Thus, the presented method becomes a boundary-only method in the sense that only boundary discretization is required. The additional collocation points inside the domain do not spoil the pure BEM character of the method. Numerical results for certain classical nonlinear problems are presented, which validate the effectiveness and the accuracy of the proposed method.

Numerical solution of distributed order fractional differential equations

In this paper a method for the numerical solution of distributed order FDEs (fractional differential equations) of a general form is presented. The method applies to both linear and nonlinear equations. The Caputo type fractional derivative is employed. The distributed order FDE is approximated with a multi-term FDE, which is then solved by adjusting appropriately the numerical method developed for multi-term FDEs by Katsikadelis. Several example equations are solved and the response of mechanical systems described by such equations is studied. The convergence and the accuracy of the method for linear and nonlinear equations are demonstrated through well corroborated numerical results.

Clamped Plates on Pasternak-Type Elastic Foundation by the Boundary Element Method

Past Due DATE : FEBRUARY 25-27, 1987 LOCATION: GOLDEN, CO TITLE: INDUSTRY-UNIVERSITY ADVANCED MATERIALS CONFERENCE INFO : DR JEROME G MORSE, ADVANCED MATERIALS INSTITUTE, COLORADO SCHOOL OF MINES, GOLDEN, CO 80401 TEL 303 273 3852 DATE : MARCH 1-5, 1987 LOCATION: HOUSTON, TX ABSTRACT: No Info TITLE: 6TH INTL SYMP ON OFFSHORE MECHANICS AND ARTIC ENGINEERING INFO : AMERICAN SOCIETY OF MECHANICAL ENGINEERS, UNITED ENGINEERING CENTER 345 E 47TH STREET, NEW YORK, NY 10017 DATE : MARCH 2-6, 1987 LOCATION: BEER-SHEVA, ISRAEL ABSTRACT: Past Due TITLE: 5TH BEER-INTERNATIONAL SEMINAR ON MHD FLOWS AND TURBULENCE INFO : PROF H BRANOVER, CENTER FOR MHD STUDIES, BEN-GURION UNIVERSITY OF THE NEGEV, BEER-SHEVA 85105, ISRAEL DATE : MARCH 18-20, 1937 LOCATION: CAMBRIDGE, UK ABSTRACT: No Info TITLE: EUROMECH 220: MIXING AND CHEMICAL REACTIONS IN TURBULENT FLOWS INFO : PROF K N C BRAY, UNIVERSITY ENGINEERING DEPARTMENT, TRUMPINGTON ST, CAMBRIDGE, CB2 1PZ UK DATE : MARCH 22-26, 1987 LOCATION: SAN ANTONIO, TX ABSTRACT: 8/1/36 TITLE: FOURTH INT. CONF. ON NUMERICAL METHODS IN FRACTURE MECHANICS INFO : M.F. KANNINEN, ENGIN. AND MAT. SCIENCE DIV., SOUTHWEST RESEARCH INST., PO DRAWER 28510, SAN ANTONIO, TX 78284 TEL: 512-522-3248 OATE : APRIL 6-8, 1987 LOCATION: GHENT, BELGIUM ABSTRACT: Past Due TITLE: INTERNATIONAL CONFERENCE ON STABILITY OF PLATE AND SHELL STRUCTURES INFO : D VANDEPITTE, GROTESTEENWEG-NORD 2, B-9710 ZWIJNAARDE, BELGIUM DATE : APRIL 6-8, 1987 LOCATION: MONTEREY, CA ABSTRACT: 8/22/86 TITLE: 28TH AIAA STRUCTURES, STRUCTURAL DYNAMICS, AND MATERIALS CONFERENCE INFO : DR. KEITH T. KEDWARD, ALCOA DEFENSE SYSTEMS, INC., 16761 VIA DEL CAMPO COURT, SAN DIEGO, 92127 TEL: 619-695-2260 DATE : APRIL 6-9, 1987 LOCATION: LONDON, ENGLAND ABSTRACT: 7/1/86 TITLE: 5TH INTERNATIONAL MODAL ANALYSIS CONFERENCE INFO : DOMINICK J. DEMICHELE, UNION COLLEGE, GRADUATE S CONTINUING STUDIES, WELLS HOUSE 1 UNION AVENUE, SCHENECTADY, NY 12308 TEL:518-370-6288 DATE : APRIL 6-10, 1987 LOCATION: BARCELONA, SPAIN ABSTRACT: No Info TITLE: INT CONF ON COMPUTATIONAL PLASTICITY INFO : D R J OWEN, DEPT OF CIVIL ENGINEERING, UNIVERSITY COLLEGE OF SWANSEA, SINGLETON PARK, SWANSEA SA2 8PP, UK DATE : APRIL 7-8, 1987 LOCATION: GLASGOW, SCOTLAND ABSTRACT: No Info TITLE: APPLIED SOLID MECHANICS CONFERENCE INFO : A S TOOTH, DEPARTMENT OF MECHANICS OF MATERIALS, UNIVERSITY OF STRATHCLYDE, 75 MONTROSE ST, GLASGOW Gl 1XJ UK ABSTRACT: 8/22/86 DATE : APRIL 9-10, 1987 LOCATION: MONTEREY, CA TITLE: AIAA DYNAMICS SPECIALISTS CONFERENCE INFO : ANTHONY F. MESSINA, DEPT. 76-12, LOCKHEED-CALIFORNIA CO., P.O. BOX 551, BURBANK, CA 91520 TEL: 818-847-4910 8/22/86 DATE : APRIL 9-10, 1987 LOCATION: MONTEREY, CA TITLE: AIAA DYNAMICS SPECIALISTS CONFERENCE INFO : ANTHONY F. MESSINA, DEPT. 76-12, LOCKHEED-CALIFORNIA CO., P.O. BOX 551, BURBANK, CA 91520 TEL: 818-847-4910 DATE : APRIL 13-15, 1987 LOCATION: UNIVERSITY PARK,PA ABSTRACT: Past Due TITLE: INTERNATIONAL CONFERENCE ON ENVIRONMENTAL DEGRADATION OF MATERIALS INFO : R P MCNITT, 227 HAMMOND BUILDING, UNIVERSITY PARK, PA 16802 OATE : APRIL 13-16, 1987 LOCATION: SAN ANTONIO, TX ABSTRACT: Past Due TITLE: IUTAM SYMPOSIUM ON ADVANCED BOUNDARY ELEMENT METHODS INFO : DR T A CRUSE, SOUTHWEST RESEARCH INSTITUTE, P 0 DRAWER 28510, SAN ANTONIO, TX 78284 TEL 512 684 5111 DATE : APRIL 26-30, 1987 LOCATION: CINCINNATI, OH ABSTRACT: 6/1/86 TITLE: SYM. ON COMPOSITE MATERIALS: FATIGUE AND FRACTURE, 9TH SYM. (ASTM) INFO : PAUL A. LAGACE, MIT, ROOM 33-313, CAMBRIDGE, MA 02139 TEL: 617-253-3628 DATE : APRIL 26-30, 1987 LOCATION: CINCINNATI, OH ABSTRACT: 6/1/86 TITLE: MECHANICAL RELAXATION OF RESIDUAL STRESSES (ASTM) INFO : LEONARD MORDFIN, NATIONAL BUREAU OF STANDARDS, B344 MATERIALS BUILDING, GAITHERSBURG, MD 20899 DATE : APRIL 28-MAY 1, 1987 LOCATION: UXBRIDGE, UK ABSTRACT: Past Due TITLE: MAFELAP 1987:C0NF ON THE MATHEMATICS OF FINITE ELEMENTS 8 APPLICATIONS INFO : SECRETARY, INSTITUTE OF COMPUTATIONAL MATHEMATICS, BRUNEL UNIVERSITY, UXBRIDGE, MIDDLESEX, UB8 3PH UK Journal of Applied Mechanics DECEMBER 1986, Vol. 53/917 Downloaded 12 Aug 2010 to 146.6.92.224. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

Non-linear dynamic analysis of beams with variable stiffness

Abstract In this paper the analog equation method (AEM), a BEM-based method, is employed to the non-linear dynamic analysis of a Bernoulli–Euler beam with variable stiffness undergoing large deflections, under general boundary conditions which maybe non-linear. As the cross-sectional properties of the beam vary along its axis, the coefficients of the differential equations governing the dynamic equilibrium of the beam are variable. The formulation is in terms of the displacements. The governing equations are derived in both deformed and undeformed configuration and the deviations of the two approaches are studied. Using the concept of the analog equation, the two coupled non-linear hyperbolic differential equations with variable coefficients are replaced by two uncoupled linear ones pertaining to the axial and transverse deformation of a substitute beam with unit axial and bending stiffness, respectively, under fictitious time-dependent load distributions. A significant advantage of this method is that the time history of the displacements as well as the stress resultants are computed at any cross-section of the beam using the respective integral representations as mathematical formulae. Beams with constant and varying stiffness are analyzed under various boundary conditions and loadings to illustrate the merits of the method as well as its applicability, efficiency and accuracy.

Buckling of plates with variable thickness—an analog equation solution

Abstract In this paper the analog equation method (AEM) is applied to buckling analysis of plates with variable thicknss. According to this method the displacement and its derivatives in the fourth order partial differential equation with variable coefficients are expressed in terms of a fictitious load which is established from the integral equation solution of an adjoint analog equation. The orginal eigenvalue problem for a differential equation of buckling is converted into a typical linear eigenvalue problem for the discrete values of the fictitious load, from which the buckling loads are established numerically. Numerical results are presented which illustrate the effectiveness of the proposed method.

The BEM for numerical solution of partial fractional differential equations

A numerical method is presented for the solution of partial fractional differential equations (FDEs) arising in engineering applications and in general in mathematical physics. The solution procedure applies to both linear and nonlinear problems described by evolution type equations involving fractional time derivatives in bounded domains of arbitrary shape. The method is based on the concept of the analog equation, which in conjunction with the boundary element method (BEM) enables the spatial discretization and converts a partial FDE into a system of coupled ordinary multi-term FDEs. Then this system is solved using the numerical method for the solution of such equations developed recently by Katsikadelis. The method is illustrated by solving second order partial FDEs and its efficiency and accuracy is validated.

Elastic deformation of ribbed plates under static, transverse and inplane loading

Abstract In this paper the analysis of ribbed plate systems subjected to transverse and inplane loading is presented. The adopted model takes into account the resulting inplane forces and deformations of the plate as well as the axial forces and deformations of the beam, due to combined response of the system. The analysis consists in isolating the beams from the plate by sections parallel to the lower outer surface of the plate. The forces at the interface, which produce lateral deflection and inplane deformation to the plate and lateral deflection and axial deformation to the beam, are established using continuity conditions at the interface. The solution of the arising plate and beam problems which are nonlinearly coupled, is achieved using the analog equation method. The adopted model permits the evaluation of the shear forces at the interface, the knowledge of which is very important in designing prefabricated ribbed plates. The influence of the inplane loading as well as the inplane geometrical boundary conditions on the deflections of the plate–beams system, and the shear forces at the interfaces between the plate and the beams is investigated by numerical examples of great practical interest.

Large deflection analysis of plates on elastic foundation by the boundary element method

Abstract A boundary element method is developed for the large deflection analysis of thin elastic plates resting on elastic foundation. The subgrade reaction may depend linearly (Winkler-type) or nonlinearly on the deflection as well as on the point coordinates (nonhomogeneous subgrade). Moderately large deflections are examined as described by the von Karman equations. The plate may have arbitrary shape and its boundary may be subjected to any type of boundary condition. The proposed method uses the fundamental solution of the linear plate theory and treats the nonlinearities as well as the subgrade reaction as unknown domain forces. Numerical results are presented to illustrate the method and demonstrate its effectiveness and accuracy.

A BEM approach to static and dynamic analysis of plates with internal supports

A boundary element approach is developed for the static and dynamic analysis of Kirchhoffs plates of arbitrary shape which, in addition to the boundary supports, are also supported inside the domain on isolated points (columns), lines (walls) or regions (patches). All kinds of boundary conditions are treated. The supports inside the domain of the plate may yield elastically. The method uses the Greens function for the static problem without the internal supports to establish an integral representation for the solution which involves the unknown internal reactions and inertia forces within the integrand of the domain integrals. The Greens function is established numerically using BEM. Subsequently, using an effective Gauss integration for the domain integrals and a BEM technique for line integrals a system of simultaneous, in general, nonlinear algebraic equations is obtained which is solved numerically. Several examples for both the static and dynamic problem are presented to illustrate the efficiency and the accuracy of the proposed method.

On the discontinuity of the flutter load for various types of cantilevers

Abstract In this investigation, using an energy (variational) approach, the flutter instability for various types of elastically restrained uniform cantilevers carrying up to three concentrated masses and subjected to a follower compressive force, is presented. The effects of transverse shear deformation and rotatory inertia of the mass of the column and of the positioning of the concentrated masses with or without their rotational inertia, are also included in the analysis. In all cases, where the flutter load is obtained from the coincidence of the second and third flexural eigenfrequencies a discontinuity with a finite jump in this load is possible; the lower value of the flutter load at this discontinuity is obtained from the coincidence of the first and second eigenfrequencies, while the upper value of this load is obtained from the coincidence of the second and third eigenfrequencies. Subsequently, it is found that the flutter load is a sectionally continuous function of certain of the varying parameters. Finally, the effect of several parameters upon the magnitude of the jump in the flutter load, is also discussed.