Convex Analysis may be considered as a refinement of standard calculus, with equalities and approximations replaced by inequalities. As such, it can easily be integrated into a graduate study curriculum. Minimization algorithms, more specifically those adapted to non-differentiable functions, provide an immediate application of convex analysis to various fields related to optimization and operations research. These two topics making up the title of the book, reflect the two origins of the authors, who belong respectively to the academic world and to that of applications. Part I can be used as an introductory textbook (as a basis for courses, or for self-study); Part II continues this at a higher technical level and is addressed more to specialists, collecting results that so far have not appeared in books.
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Author: Andrew J. Davids and Gregory J. Hancock | Size: 1 MB | Format:PDF | Quality:Unspecified | Publisher: ASCE | Year: 1986 | pages: 17
The local buckling and post-local buckling behavior of short length
I-section columns fabricated by welding high tensile steel plate is described. Six
sections of three different section geometries were tested to destruction by loading
between rigid end plattens mounted on freely rotating bearings in a
compression testing machine. Accurate measurements of welding residual strains
and geometric imperfections were taken prior to testing and are presented in
the paper. Comparisons of the test local buckling loads are made with a finite
strip buckling analysis including welding residual strain. Comparisons of the
measured axial stiffnesses and stress distributions were made with a nonlinear
finite strip analysis, which includes geometric imperfections and welding residual
strain. The test loads are compared with those based on the Winter effective
width formulas.
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COMPRESSION TESTS OF LONG WELDED I-SECTION COLUMNS
Author: A. J. Davids and G. J. Hancock | Size: 1 MB | Format:PDF | Quality:Unspecified | Publisher: ASCE | Year: 1986 | pages: 17
The results of compression tests of long, welded I-section columns
composed of slender plates of high tensile steel are described. Tests of concentrically
loaded specimens are compared with a finite strip nonlinear analysis
model for predicting the elastic interaction of local and overall buckling of thinwalled
columns. Tests of concentrically and eccentrically loaded specimens are
compared with the proposed AISC Load and Resistance Factor Design method
for columns with slender cross sections. The column strengths are also compared
with those of compact columns of equivalent weight to demonstrate the
economies available for columns with slender cross sections.
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Slender thin cylindrical shells under unsymmetrical strip loads
Author: Adam J. Sadowski; J. Michael Rotter | Size: 2.4 MB | Format:PDF | Quality:Unspecified | Publisher: Elsevier | Year: 2012 | pages: 11
Modern procedures for the design of shell structures against buckling have their basis in analytical studies of axisymmetric shell geometries under the very simple load cases of uniform compression, external pressure and torsion. Studies of more complex but realistic stress states were based on prebuckling analyses using either membrane theory or linear bending theory because even these involved considerable mathematical complexity. As a result, only limited conclusions for practical design could be drawn and the effects of geometric nonlinearity could not be assessed. With recent advances in computing power and nonlinear finite element programs, it is now possible to undertake nonlinear analyses of complex load patterns that would have been very difficult to do only a decade or so ago.
A number of practical load cases lead to a strip of pressure down one meridian, of which the best known ones are probably wind on tanks, eccentric discharge in silos, local thermal differentials, and partial fluid filling of a cylinder. This paper explores some of the rather unexpected stress patterns and modes of buckling that are predicted to develop in thin-walled cylindrical shells under such unsymmetrical strips of normal pressure. The results of a parametric study are presented to show the influence of the circumferential spread of the pressure strip on the structural behaviour. It is shown that the structural response to such loads may be very different, depending on whether the load acts inward or outward, and whether geometric nonlinearity and geometric imperfections are also included in the assessment.
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Tanks with a conical roof are studied in this paper under wind load, for a roof which is supported
by rafters and columns. Buckling occurs in the form of deflections in the cylindrical shell and the
buckling mode is localized in the windward region. Both bifurcation analysis and geometrically
nonlinear analysis have been performed using finite element discretizations of the structure. The
wind pressures have been obtained from wind tunnel experiments performed as part of the research,
and have been obtained for tank geometries for which information was not previously available. The
results show high imperfection sensitivity of tanks with a conical roof, and buckling loads for wind
velocities in the same order as those expected to occur in the Caribbean region.
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Challenges in the computation of lower-bound buckling loads for tanks under wind pressures
Author: Eduardo M. Sosa, Luis A. Godoy | Size: 728 KB | Format:PDF | Quality:Unspecified | Publisher: Elsevier | Year: 2010 | pages: 11
This paper reports on the implementation of a lower-bound approach for the buckling of imperfection-sensitive shells using general purpose finite element codes. The stability of cylindrical steel tanks under wind pressure is evaluated for two tank configurations: conical roof tanks and open top tanks. For both tank configurations, several geometric relations are considered in order to find the variation of the knock-down factor as the geometry changes. The reduced energy method is implemented to compute a lower-bound for critical wind pressures and the results are compared with the static non-linear analysis carried out on the same models. An alternative way to implement the reduced energy method is presented to improve the results obtained with the proposed methodology
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The progress of non-linear FE-methods allows it nowadays to simulate the load-bearing behaviour
of steel shells taking geometric and material nonlinearities and imperfections into account. In this
paper it is investigated for the basic buckling case of uniform external pressure, which equivalent
geometric imperfections have to be applied in the numerical analysis (GMNIA) to achieve the
experimentally determined buckling resistances. Single longitudinal imperfections are better suited
than eigenform-affine initial deformations. Proposals for the imperfection amplitude and
imperfection width are submitted. The results are compared with the regulations of the Eurocode.
Essential modifications are discussed.
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A reduced stiffness approach for the buckling of open cylindrical tanks under wind loads
Author: Rossana C. Jacaa, Luis A. Godoyb, Fernando G. Floresb, James G.A. Croll | Size: 660 KB | Format:PDF | Quality:Unspecified | Publisher: Elsevier | Year: 2007 | pages: 10
This paper reports on the implementation of a lower bound approach to the buckling analysis of cylindrical shells for tanks subjected
to wind loads. The formulation is based on a reduced energy model of the shell adapted to a special purpose, semi-analytical, finite
element program in which it is possible to separately compute the membrane and bending energy contributions. First, the energy
components are investigated, in order to identify stabilizing and destabilizing contributions. Second, an eigenvalue analysis is carried out
using a reduced value of the stiffness, in which membrane components are eliminated on the basis that they are assumed to be eroded as a
result of mode coupling catalyzed by imperfections. The methodology is employed for thin-walled, above ground, tanks under wind
pressures. It is shown that the resulting critical loads constitute lower bounds to those obtained using a nonlinear analysis of the shell,
including imperfections, and also to those obtained from experiments.
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The wind-induced buckling of thin-walled steel cylinders, such as silos and
tanks, was investigated by wind-tunnel testing for a limited range of the
parameters. While wind-buckling of short, stocky shells can be well represented
by an equivalent uniform external pressure, long shells show quite a
different behaviour, which is strongly influenced by the axial compression
forces. This paper presents a study of this behaviour, based on numerical
analyses and considering various types of imperfection shape. The effect of
geometrical nonlinearity, as well as material plasticity, has also been
included. A comparison with test results shows good agreement with the
numerical results of imperfect shells, provided that special eigenmodeshaped
modes of imperfections are excluded.
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