C. Y. Wang

Exact solutions for buckling of structural members

The study of buckling loads, which often hinges on numerical methods, is key in designing structural elements. But the need for analytical solutions in addition to numerical methods is what drove the creation of Exact Solutions for Buckling of Structural Members. It allows readers to assess the reliability and accuracy of solutions obtained by numerical methods. The author has attempted to gather and present as many exact buckling solutions as possible in one single volume for engineers and researchers. These buckling solutions of columns, beams, arches, ring plates, and shells should serve as benchmarks for checking the validity, convergence, and accuracy of numerical methods and solutions. Catalog Copy.

Structural vibration: exact solutions for strings, membranes, beams and plates

Structural Vibration: Exact Solutions for Strings, Membranes, Beams, and Plates offers an introduction to structural vibration and highlights the importance of the natural frequencies in design. It focuses on free vibrations for analysis and design of structures and machine and presents the exact vibration solutions for strings, membranes, beams, and plates. This book emphasizes the exact solutions for free transverse vibration of strings, membranes, beams, and plates. It explains the intrinsic, fundamental, and unexpected features of the solutions in terms of known functions as well as solutions determined from exact characteristic equations. The book provides.

Exact solutions of the Navier-Stokes equations-the generalized Beltrami flows, review and extension

SummaryExact solutions of the Navier-Stokes equations are rare. This paper reviews the existing exact solutions of the generalized Beltrami flows. Several new solutions are presented.

Boundary layers on rotating cones, discs and axisymmetric surfaces with a concentrated heat source

SummaryA concentrated heat source is situated at the tip of an otherwise adiabatic rotating cone. Due to centrifugal forces, velocity and thermal boundary layers spread on the surface. After a similarity transform, the governing equations reduce to set of nonlinear, ordinary differential equations which are then integrated numerically. The related cases of rotating discs and other axisymmetric surfaces are considered.

Nonlinear streaming due to the oscillatory stretching of a sheet in a viscous fluid

SummaryAn elastic sheet is stretched back and forth in a viscous fluid. The problem is governed by a nondimensional parameterS which represents the relative magnitude of frequency to stretching rate. The Navier-Stokes equations are solved by matched asymptotic expansions for largeS. Due to nonlinearity there exists boundary layers ofO(S−1/2). The unsteady oscillatory flow contains both basic and higher harmonic oscillations. The induced steady streamlines show a saddle like flow which is different from that of acoustic streaming.

Exact vibration solution for exponentially tapered cantilever with tip mass

This technical note is concerned with the free vibration problem of a cantilever beam with constant thickness and exponentially decaying width. Existing analytical results for such a vibration beam problem are found to be incomplete because lower frequencies could not be obtained. Presented herein is the exact characteristic equation for generating the complete vibration frequencies for the considered vibrating beam problem. Also the note treated for the first time such a tapered cantilever beam with a tip mass. The exact solutions (frequencies and mode shapes) are important to engineers designing such tapered beams and the results serve as benchmarks for assessing the validity, convergence and accuracy of numerical methods and solutions.

Buckling of rectangular plates with internal hinge

This paper is concerned with the elastic buckling of uniaxially/biaxially loaded rectangular plates with an internal hinge and two opposite sides simply supported. The buckling problem is solved analytically using the Levy method. The exact buckling solutions furnished by the Levy method provide benchmark solutions for such plates with an internal hinge. Extensive buckling results are presented for plates of a wide range of aspect ratios, hinge locations and in-plane loading configurations. Based on these results, the buckling behaviour of plates with an internal hinge may be observed with respect to the aforementioned design parameters.

BUCKLING OF STANDING VERTICAL PLATES UNDER BODY FORCES

This paper is concerned with the elastic buckling problem of vertical plates under body forces/selfweight. The vertical plate is either clamped or simply supported at its bottom edge while its top edge is free. The two sides of the plate may either be free, simply supported or clamped. For plates with simply supported sides, exact critical buckling solutions are derived using the Levy approach. For other boundary conditions, accurate buckling solutions are obtained for very wide plates to very tall plates using the Ritz method.

Global buckling load of a nonlinearly elastic bar

SummaryThe nonlinear buckling of an elastic bar with softening characteristic is studied. It is found that, under large disturbances, the bar may buckle under loads well below the linear buckling load.

Slow rotation of a disc in a fluid-filled casing

SummaryStokes flow due to a rotating disc enclosed by a casing is solved by eigenfunction expansion and collocation. The method is simpler than approximate methods using dual integral equations or full numerical integration. The torque is determined for various casing dimensions.