This paper deals with the continuous classical optimal control problem for triple partial differential equations of parabolic type with initial and boundary conditions; the Galerkin method is used to prove the existence and uniqueness theorem of the state vector solution for given continuous classical control vector. The proof of the existence theorem of a continuous classical optimal control vector associated with the triple linear partial differential equations of parabolic type is given. The derivation of the Fréchet derivative for the cost function is obtained. At the end, the theorem of the necessary conditions for optimality of this problem is stated and is proved.

A long-span Prestressed Concrete Hunched Beam with Multi-Opening has been developed as an alternative to steel structural elements. The commercial finite element package ABAQUS/CAE version 2019 has been utilized. This article has presented the results of three-dimensional numerical simulations investigating the flexural behaviour of existing experimental work of supported Prestressed Concrete Hunched Beams with multiple openings of varying shapes under static monotonic loads. Insertion openings in such a beam lead to concentrate stresses at the corners of these openings; as a result, extensive cracking would appear. Correlation between numerical models and empirical work has also been discussed regarding load displacemen

      It is useful to analyze any optical system theoretically before proceeding with its design in order to ensure the effectiveness of the design through computer simulations that are important and useful in designs for the ability to predict the performance of solar concentrator under any conditions.  For this design, non-sequential ray tracing mode wasused in the Zimax program with a light source that simulated solar radiation.  The purpose of the design of a compound parabolic concentrator (CPC) is to take advantage of the solar radiation that falls on it without the need for an efficiently tracked system within certain limits of the angle of solar radiation fall known as the acceptance angle.&nbsp

A few examinations have endeavored to assess a definitive shear quality of a fiber fortified polymer (FRP)- strengthened solid shallow shafts. Be that as it may, need data announced for examining the solid profound pillars strengthened with FRP bars. The majority of these investigations don't think about the blend of the rigidity of both FRP support and cement. This examination builds up a basic swagger adequacy factor model to evaluate the referenced issue. Two sorts of disappointment modes; concrete part and pulverizing disappointment modes were examined. Protection from corner to corner part is chiefly given by the longitudinal FRP support, steel shear fortification, and cement rigidity. The proposed model has been confirmed util

In this research a theoretical study has been carried out on the behavior and strength of simply supported composite beams strengthened by steel cover plate taking into consideration partial interaction of shear connectors and nonlinear behavior of the materials and shear connectors. Following the procedure that already has been adopted by Johnson (1975), the basic differential equations of equilibrium and compatibility were reduced to single differential equation in terms of interface slip between concrete slab and steel beam. Furthermore, in order to consider the nonlinear behavior of steel, concrete and shear connectors, the basic equation was rearranged so that all terms related to materials are isol

In this paper, effective slab width for the composite beams is investigated with special emphasis on the effect of web openings. A three dimensional finite element analysis, by using finite element code ANSYS, is employed to investigate shear lag phenomenon and the resulting effective slab width adopted in the classical T-beam approach. According to case studies and comparison with limitations and rules stipulated by different standards and codes of practice it is found that web openings presence and panel proportion are the most critical factors affecting effective slab width, whereas concrete slab thickness and steel beam depth are less significant. The presence of web opening reduces effective slab width by about 21%.

The design, construction and investigation of experimental study of two compound parabolic concentrators (CPCs) with tubular absorber have been presented. The performance of CPCs have been evaluated by using outdoor experimental measurements including the instantaneous thermal efficiency. The two CPCs are tested instantly by holding them on a common structure. Many tests are conducted in the present work by truncating one of them in three different levels. For each truncation the acceptance half angle (θ_c) was changed. Geometrically, the acceptance half angle for standard CPC is (26^o). For the truncation levels for the other CPC 1, 2 and 3 the acceptance half angle were 20^o, 26^o and 5

This paper presents experimentally a new configuration of shear connector for Steel-Concrete-Steel (SCS) sandwich beams that is derived from truss configuration. It consists of vertical and inclined shear connectors welded together and to cover steel plates infilled with concrete. Nine simply supported SCS beams were tested until the failure under a concentrated central load (three- point bending). The beams were similar in length (1100mm), width (100mm), and the top plate thickness (4mm). The test parameters were; beam thickness (150, 200, 250, and 300mm), the bottom plate thickness (4, and 6mm), the diameter of the shear connectors (10, 12, and 16mm), and the connector spacing (100, 200, and 250mm). The test results sh