Critical buckling and natural frequencies behavior of laminated composite thin plates subjected to in-plane uniform load is obtained using classical laminated plate theory (CLPT). Analytical investigation is presented using Ritz- method for eigenvalue problems of buckling load solutions for laminated symmetric and anti-symmetric, angle and cross ply composite plate with different elastic supports along its edges. Equation of motion of the plate was derived using principle of virtual work and solved using modified Fourier displacement function that satisfies general edge conditions. Various numerical investigation were studied to exhibit a convergence and accuracy of the present solution for considering some design parameters such as edge

       In this work, we prove that the triple linear partial differential equations (PDEs) of elliptic type (TLEPDEs) with a given classical continuous boundary control vector (CCBCVr) has a unique "state" solution vector (SSV)  by utilizing the Galerkin's method (GME). Also, we prove the existence of a classical continuous boundary optimal control vector (CCBOCVr) ruled by the TLEPDEs. We study the existence solution for the triple adjoint equations (TAJEs) related with the triple state equations (TSEs). The Fréchet derivative (FDe) for the objective function is derived. At the end we prove the necessary "conditions" theorem (NCTh) for optimality for the problem.

The researcher [1-10] proposed a method for computing the numerical solution to quasi-linear parabolic p.d.e.s using a Chebyshev method. The purpose of this paper is to extend the method to problems with mixed boundary conditions. An error analysis for the linear problem is given and a global element Chebyshev method is described. A comparison of various chebyshev methods is made by applying them to two-point eigenproblems. It is shown by analysis and numerical examples that the approach used to derive the generalized Chebyshev method is comparable, in terms of the accuracy obtained, with existing Chebyshev methods.

This study is concerned with the derivation of differential equation of motion for the free coupled vertical – torsional and lateral vibration of opened thin-walled curved beams. The curved beam to be considered in this study is of isotropic opened thin – walled (I) section with equal top and bottom flanges. The derivation depends on Hamilton's principle which required finding the potential and kinetic energy of the curved beam section due to internal stresses and all types of movements (Vertical,Torsional and Lateral) .The effect of restrained warping displacement is also considered in this study. Three differential equations are derived for vertical, torsional and lateral movement .and approximate solutions are developed by using the

Free cement refractory concrete is a type of refractory concrete with replacing alumina cement by bonding materials such as white kaolin, red kaolin and fumed silica. The free cement refractory concrete used in many applications like Petrochemicals, iron furnaces and cement production industries. The research clarifies the effect of steel fibers with two types crimped steel fibers and hooked steel
fibers with percentages 0.5%, 1% and 1.5% by volume from weight of bauxite aggregates. The additions of steel fibers with two types gave good properties in high temperatures where the specimens keep the dimension without failure and the properties made the best. the percentage of increasing for thermal conductivity was 44% for 1.5% crimped

Solvents are important components in the pharmaceutical and chemical industries, and they are increasingly being used in catalytic reactions. Solvents have a significant influence on the kinetics and thermodynamics of reactions, and they can significantly change product selectivity. Solvents can influence product selectivity, conversion rates, and reaction rates. However, solvents have received a lot of attention in the field of green chemistry. This is due to the large amount of solvent that is frequently used in a process or formulation, particularly during the purification steps. However, neither the solvent nor the active ingredient in a formulation is directly responsible for the reaction product's composition. Because these ch