18 research outputs found
IFM and Its Dual Form for Eigen Value Analysis of Plate Bending Problems
Integrated Force Method (IFM) is now well accepted
method for the analysis of framed and continuum structure
problems under static and dynamic loading. The methodology
proposed in the present paper attempts to calculate the frequency
using the force based eigen value analysis, while the present
literature emphasizes on displacement based eigen value analysis.
The suggested formulation is based on the Cauchy's equilibrium
operator, Saint Venant's compatibility operator and Hooke's
material matrix operator. Element equilibrium and flexibility
matrices are derived by discretizing the expression of potential
and complimentary strain energies respectively. The displacement
field is decided using Hermits interpolation function, while the
stress field is approximated using the traditional polynomial of
approximate order. Formulation developed earlier for static analysis
using rectangular element having nine force degree of freedom
and twelve displacement degree of freedom (RECT 9F 12D)
is extended. Lumped mass and consistent mass matrices are
also derived. A modified formulation of IFM which is named
as Dual Integrated Force Method (DIFM) is also explored. Plate
bending problems with two different boundary conditions are
attempted. Various discretization patterns are used to check the
convergence of frequency values towards the analytical solution.
Results obtained for natural frequencies, force mode shapes for
each frequency value and corresponding nodal displacements are
presented. Results obtained for natural frequency are compared
with the exact solution; a good agreement is found
From simplicial Chern-Simons theory to the shadow invariant II
This is the second of a series of papers in which we introduce and study a
rigorous "simplicial" realization of the non-Abelian Chern-Simons path integral
for manifolds M of the form M = Sigma x S1 and arbitrary simply-connected
compact structure groups G. More precisely, we introduce, for general links L
in M, a rigorous simplicial version WLO_{rig}(L) of the corresponding Wilson
loop observable WLO(L) in the so-called "torus gauge" by Blau and Thompson
(Nucl. Phys. B408(2):345-390, 1993). For a simple class of links L we then
evaluate WLO_{rig}(L) explicitly in a non-perturbative way, finding agreement
with Turaev's shadow invariant |L|.Comment: 53 pages, 1 figure. Some minor changes and corrections have been mad
(Re)constructing Dimensions
Compactifying a higher-dimensional theory defined in R^{1,3+n} on an
n-dimensional manifold {\cal M} results in a spectrum of four-dimensional
(bosonic) fields with masses m^2_i = \lambda_i, where - \lambda_i are the
eigenvalues of the Laplacian on the compact manifold. The question we address
in this paper is the inverse: given the masses of the Kaluza-Klein fields in
four dimensions, what can we say about the size and shape (i.e. the topology
and the metric) of the compact manifold? We present some examples of
isospectral manifolds (i.e., different manifolds which give rise to the same
Kaluza-Klein mass spectrum). Some of these examples are Ricci-flat, complex and
K\"{a}hler and so they are isospectral backgrounds for string theory. Utilizing
results from finite spectral geometry, we also discuss the accuracy of
reconstructing the properties of the compact manifold (e.g., its dimension,
volume, and curvature etc) from measuring the masses of only a finite number of
Kaluza-Klein modes.Comment: 23 pages, 3 figures, 2 references adde
p-form spectra and Casimir energies on spherical tesselations
Casimir energies on space-times having the fundamental domains of
semi-regular spherical tesselations of the three-sphere as their spatial
sections are computed for scalar and Maxwell fields. The spectral theory of
p-forms on the fundamental domains is also developed and degeneracy generating
functions computed. Absolute and relative boundary conditions are encountered
naturally. Some aspects of the heat-kernel expansion are explored. The
expansion is shown to terminate with the constant term which is computed to be
1/2 on all tesselations for a coexact 1-form and shown to be so by topological
arguments. Some practical points concerning generalised Bernoulli numbers are
given.Comment: 43 pages. v.ii. Puzzle eliminated, references added and typos
corrected. v.iii. topological arguments included, references adde
Towards Optimal Design of Steel- Concrete Composite Plane Frames using a Soft Computing Tool
The use of steel – concrete composite elements in a multistoried building increases the speed of construction and reduces the overall cost. The optimum design of composite elements such as slabs, beams and columns can further reduce the cost of the building frame. In the present study, therefore, Genetic Algorithm (GA) based design optimization of steel concrete composite plane frame is addressed with the aim of minimizing the overall cost of the frame. The design is carried out based on the limit state method using recommendations of IS 11834, EC 4 and BS 5950 codes and Indian and UK design tables. The analysis is carried out using computer- oriented direct stiffness method. A GA based optimization software, with pre- and postprocessing capabilities, has been developed in Visual Basic.Net environment. To validate the implementation, examples of 2 × 3 and 2 × 5 composite plane frames are included here along with parametric study