Page 39 - ASME AM3D/IDETC/CIE 2015 Program
P. 39
IDETC/CIE
KEYNOTE & PLENARY LECTURES
MSNDC/VIB KEYNOTES worked near the border between mechanics and applied
mathematics ever since.
Tuesday, August 4
SESSION: MSNDC-18-1 After receiving his doctorate in 1965 under the direction of W. H.
Warner, Antman accepted a post-doctoral position at the Courant
2:00PM – 3:00PM
Institute of New York University. There J. B. Keller and he edited the
Location: Room 302, Level 3 book Bifurcation Theory and Nonlinear Eigenvalue Problems.
In 1972, Antman accepted a professorship in the Department of
Stuart S. Antman Mathematics at the University of Maryland, where he is now a
Distinguished University Research Professor in the Department of
2015 Lyapunov Award Recipient Mathematics, the Institute for Physical Science and Technology, and
University of Maryland the Institute for Systems Research. During the intervening years, he
has held visiting appointments in Oxford, Edinburgh, Paris, Orsay,
Palaiseau, Bonn, Darmstadt, Dortmund, Leipzig, Budapest, Rome,
EFFECTS OF NONLINEAR MATERIAL RESPONSE ON Providence, Hong Kong, and Mexico City.
THE DYNAMICS AND STABILITY OF STRUCTURES Antman’s doctoral thesis and a handful of subsequent papers were
Abstract: Many analytical and numerical models for structures are devoted to the derivation of geometrically exact nonlinear theories of
based on the use of linear stress-strain laws and the use of simple rods and shells (and the resolution of associated paradoxes). The
models for dissipative mechanisms. For structures that can suffer knowledge he gained from writing up the invited contributions to
large deformations and that are subject to live or dynamical loads, Bifurcation Theory formed the foundation of his subsequent work on
very slight changes in constitutive functions (such as replacing a the global bifurcation and buckling of nonlinearly elastic rods and
linear function with a nearby nonlinear function) could produce large shells. In the 1980’s, Antman’s work branched out to encompass
changes in the behavior of solutions to the governing equations of shock structure in solids, dynamical (visco)-elasto-plasticity,
motion. This lecture describes the effect of properly invariant electro-magneto-elasticity, the dynamics of heavily-burdened
constitutive equations, accounting for nonlinear elastic, viscous, and deformable bodies, steady-state and dynamical fluid-solid interac-
plastic effects, on the behavior of solutions of geometrically exact tions, nonlinear oscillations and stability of structures, optimal control,
equations of motion for deformable solids. In particular, for many attractors for the motions of nonlinearly viscoelastic solids, blowup of
concrete problems there are thresholds in nonlinear material solutions in time, and dynamical analysis of quasistatic motions. The
response separating qualitatively different behaviors of solutions. features common to this research are the use of geometrically exact
Among the phenomena to be discussed are self-sustained oscilla- descriptions (so that no sin x is ever approximated by x) and the use of
tions, parametric resonance, blowup, snap buckling, attractors for general, properly invariant constitutive functions. As a consequence,
heavily-burdened bodies, and shock structure. this research often exhibits thresholds in material response separat-
ing qualitatively different behavior.
Antman is the author of Nonlinear Problems of Elasticity and The
Biography: Stuart Antman was an undergraduate at Rensselaer Theory of Rods in the Handbuch der Physik. He has served on the
Polytechnic Institute, where he entered the Mechanical Engineer- editorial boards of several journals on applied mathematics and on
ing program. After taking a semester of an introductory course on mechanics, having been editor-in-chief of the Archive for Rational
Mechanical Engineering, which was devoted mostly to the Mechanics and Analysis for a decade. He is currently co-editor-in-
dynamics of the middle shaft of a 10-foot-long demonstration chief of three Springer book series on applied mathematics. He is a
slide rule, he switched to a major in mathematics with the encour- Guggenheim fellow, an inaugural fellow of the Society for Industrial
agement of his Calculus professor W. E. Boyce. The mathemat- and Applied Mathematics, an inaugural fellow of the American
ics program required sophomore majors to take a course in Mathematical Society, a winner of the L. R. Ford Award of the
Theoretical Mechanics (à la Synge & Griffith) given by C. C. Mow, Mathematical Association of America, and a winner of the von
which so fascinated Antman that he undertook a heavy minor in Kármán Prize of the Society for Industrial and Applied Mathematics.
Mechanics. His fascination was increased by a senior-level
course given by G. H. Handelman covering Cartesian tensor
analysis, calculus of variations, linear elasticity, fluid dynamics
and electromagnetism, together with representative steady-state
and dynamical problems from each field. Antman’s love of
mechanics sent him to the graduate program in Aeronautics and
Engineering Mechanics at the University of Minnesota. There his
background in mechanics allowed him to take an extensive minor
in mathematics oriented toward differential equations. He has
39
KEYNOTE & PLENARY LECTURES
MSNDC/VIB KEYNOTES worked near the border between mechanics and applied
mathematics ever since.
Tuesday, August 4
SESSION: MSNDC-18-1 After receiving his doctorate in 1965 under the direction of W. H.
Warner, Antman accepted a post-doctoral position at the Courant
2:00PM – 3:00PM
Institute of New York University. There J. B. Keller and he edited the
Location: Room 302, Level 3 book Bifurcation Theory and Nonlinear Eigenvalue Problems.
In 1972, Antman accepted a professorship in the Department of
Stuart S. Antman Mathematics at the University of Maryland, where he is now a
Distinguished University Research Professor in the Department of
2015 Lyapunov Award Recipient Mathematics, the Institute for Physical Science and Technology, and
University of Maryland the Institute for Systems Research. During the intervening years, he
has held visiting appointments in Oxford, Edinburgh, Paris, Orsay,
Palaiseau, Bonn, Darmstadt, Dortmund, Leipzig, Budapest, Rome,
EFFECTS OF NONLINEAR MATERIAL RESPONSE ON Providence, Hong Kong, and Mexico City.
THE DYNAMICS AND STABILITY OF STRUCTURES Antman’s doctoral thesis and a handful of subsequent papers were
Abstract: Many analytical and numerical models for structures are devoted to the derivation of geometrically exact nonlinear theories of
based on the use of linear stress-strain laws and the use of simple rods and shells (and the resolution of associated paradoxes). The
models for dissipative mechanisms. For structures that can suffer knowledge he gained from writing up the invited contributions to
large deformations and that are subject to live or dynamical loads, Bifurcation Theory formed the foundation of his subsequent work on
very slight changes in constitutive functions (such as replacing a the global bifurcation and buckling of nonlinearly elastic rods and
linear function with a nearby nonlinear function) could produce large shells. In the 1980’s, Antman’s work branched out to encompass
changes in the behavior of solutions to the governing equations of shock structure in solids, dynamical (visco)-elasto-plasticity,
motion. This lecture describes the effect of properly invariant electro-magneto-elasticity, the dynamics of heavily-burdened
constitutive equations, accounting for nonlinear elastic, viscous, and deformable bodies, steady-state and dynamical fluid-solid interac-
plastic effects, on the behavior of solutions of geometrically exact tions, nonlinear oscillations and stability of structures, optimal control,
equations of motion for deformable solids. In particular, for many attractors for the motions of nonlinearly viscoelastic solids, blowup of
concrete problems there are thresholds in nonlinear material solutions in time, and dynamical analysis of quasistatic motions. The
response separating qualitatively different behaviors of solutions. features common to this research are the use of geometrically exact
Among the phenomena to be discussed are self-sustained oscilla- descriptions (so that no sin x is ever approximated by x) and the use of
tions, parametric resonance, blowup, snap buckling, attractors for general, properly invariant constitutive functions. As a consequence,
heavily-burdened bodies, and shock structure. this research often exhibits thresholds in material response separat-
ing qualitatively different behavior.
Antman is the author of Nonlinear Problems of Elasticity and The
Biography: Stuart Antman was an undergraduate at Rensselaer Theory of Rods in the Handbuch der Physik. He has served on the
Polytechnic Institute, where he entered the Mechanical Engineer- editorial boards of several journals on applied mathematics and on
ing program. After taking a semester of an introductory course on mechanics, having been editor-in-chief of the Archive for Rational
Mechanical Engineering, which was devoted mostly to the Mechanics and Analysis for a decade. He is currently co-editor-in-
dynamics of the middle shaft of a 10-foot-long demonstration chief of three Springer book series on applied mathematics. He is a
slide rule, he switched to a major in mathematics with the encour- Guggenheim fellow, an inaugural fellow of the Society for Industrial
agement of his Calculus professor W. E. Boyce. The mathemat- and Applied Mathematics, an inaugural fellow of the American
ics program required sophomore majors to take a course in Mathematical Society, a winner of the L. R. Ford Award of the
Theoretical Mechanics (à la Synge & Griffith) given by C. C. Mow, Mathematical Association of America, and a winner of the von
which so fascinated Antman that he undertook a heavy minor in Kármán Prize of the Society for Industrial and Applied Mathematics.
Mechanics. His fascination was increased by a senior-level
course given by G. H. Handelman covering Cartesian tensor
analysis, calculus of variations, linear elasticity, fluid dynamics
and electromagnetism, together with representative steady-state
and dynamical problems from each field. Antman’s love of
mechanics sent him to the graduate program in Aeronautics and
Engineering Mechanics at the University of Minnesota. There his
background in mechanics allowed him to take an extensive minor
in mathematics oriented toward differential equations. He has
39
