Sharif Digital Repository

The fracture phenomenon is defined via the change of state of structure (entity) between the intact and the fractured end states as the function of the state variable. The twin state functions are defined for the transition of unit of the entity between its two end states. The state ratio is defined as the ratio of the two state functions. The property of the cracked structure is defined as the product of the structure property and the state ratio. The work is then used to derive the main parameters of the fracture mechanics. The work is verified via five examples. © 2016, Springer-Verlag Berlin Heidelberg  

Beam, column, plate, and any other structure, under full or partial compressive loading, are prone to failure by the buckling phenomenon. At the instant of failure, the structure may be in unpredictable elastic, elastic–plastic, full plastic, cracked, or other forms of deterioration state. Therefore, in spite of so much study, there is no definite solution to the problem. In this paper a unified, simple, and exact theory is proposed where buckling is considered as the change of state of structure between intact and collapsed states, and then the buckling capacity is innovatively expressed via states and phenomena functions, which are explicitly defined as functions of state variable. The... 

The conventional energy release rate approach to the computation of the crack compliance in rotors is critically reviewed and its shortcoming is highlighted. The state functions and the generic compliance are introduced, defined, and verified. The proposed functions are defined based on the end states' conditions and are exact. The crack compliance of the shaft in torsion is explicitly defined as the function of the crack depth ratio and recommended as a good alternative to the classical procedure of the energy release rate method. The accuracy and efficiency of the work are verified by concise mathematical formulation and comparison of the results of the work with the others in four... 

Based on the mathematical similarity of the Schrödinger and Helmholtz equations, the tight-binding method has been employed for solving optical waveguide problems, in a manner similar to the methods commonly used in solid-state physics. The solutions (TE mode electric field waveforms and propagation constants) of a single dielectric slab waveguide are considered to be known, and tight-binding is used to compute the propagation constants of several multi-waveguide structures. Analytical solutions are derived for linear and circular arrays of adjacent waveguides. The problem of two similar adjacent waveguides is treated in detail for two cases of similar and different propagation constants of... 

Free electron lasers have been the subject of intensive interest during the recent decades. In this paper, free electron laser having sheet electron beam with arbitrary inhomogeneous profile of transverse distribution of the beam current density is studied in the linear regime, whereas a novel approach based on the Legendre polynomial expansion of eigenfunctions, already used in analyzing optical structures including stratified structures and diffraction gratings, is adapted to find the eigenfunctions and eigenvalues of the structure. As for this method is unconditionally stable, it works pretty well even in those cases in which the conventional transfer matrix method suffers from numerical... 

Three-dimensional vectorial diffraction analysis of phase and amplitude gratings in conical mounting is presented based on Legendre expansion of electromagnetic fields. In the so-called conical mounting, different fields components are coupled and the solution is not separable in terms of independent TE and TM cases. In contrast to conventional RCWA in which the solution is obtained using state variables representation of the coupled wave amplitudes by expanding space harmonic amplitudes of the fields in terms of the eigenfunctions and eigenvectors of the coefficient matrix defined by rigorous coupled wave equations, here the solution of first order coupled Maxwell's equations is expanded in...