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