The Wang-Ball polynomials operational matrices of the derivatives are used in this study to solve singular perturbed second-order differential equations (SPSODEs) with boundary conditions. Using the matrix of Wang-Ball polynomials, the main singular perturbation problem is converted into linear algebraic equation systems. The coefficients of the required approximate solution are obtained from the solution of this system. The residual correction approach was also used to improve an error, and the results were compared to other reported numerical methods. Several examples are used to illustrate both the reliability and usefulness of the Wang-Ball operational matrices. The Wang Ball approach has the ability to improve the outcomes by minimizing the degree of error between approximate and exact solutions. The Wang-Ball series has shown its usefulness in solving any real-life scenario model as first- or second-order differential equations (DEs).
In this research, the results of the Integral breadth method were used to analyze the X-ray lines to determine the crystallite size and lattice strain of the zirconium oxide nanoparticles and the value of the crystal size was equal to (8.2nm) and the lattice strain (0.001955), and then the results were compared with three other methods, which are the Scherer and Scherer dynamical diffraction theory and two formulas of the Scherer and Wilson method.the results were as followsScherer crystallite size(7.4nm)and lattice strain(0.011968),Schererdynamic method crystallite size(7.5 nm),Scherrer and Wilson methodcrystallite size( 8.5nm) and lattice strain( 0.001919).And using another formula for Schearer and Wilson methodwe obtain the size of the c
... Show MoreIn this paper, three types of epoxy-based coatings (Polyamide, pure Polyamine, and Polyamine reinforced by glass-flake) used as a lining for potable water tanks were studied using experimental and finite element methods. Tensile, impact, and fatigue tests were conducted on uncoated and coated AISI 316 stainless steel. The test results show that the applied epoxy based coating improves the mechanical properties, increases of fatigue crack resistance, and enhance the dynamic fracture toughness. The fatigue crack propagation is influenced by the compositions of epoxy coating, and the glass-flake improves the coating resistance to fatigue crack propagation compared to other types.
Jumping ability is a fundamental variable in many sports, as its execution requires an integration of muscular strength Q1 and certain biomechanical variables. This is particularly evident in gymnastics jumping events and jump shots in ball games, both of which rely on a high level of vertical resistance. Vertical resistance serves as an indicator of an athlete’s ability to overcome their body weight while counteracting gravitational force to achieve optimal performance. As such, it is considered one of the key factors in movements that demand explosive power and speed. The researchers believe that despite the significant relationship between vertical resistance, speed-strength of the arms and legs, and certain biomechanical varia
... Show MoreThe Ground Penetrating Radar (GPR) is frequently used in pavement engineering
for road pavement inspection. The main objective of this work is to validate
nondestructive, quick and powerful measurements using GPR for assessment of subgrade
and asphalt /concrete conditions. In the present study, two different antennas
(250, 500 MHz) were used. The case studies are presented was carried in University
of Baghdad over about 100m of paved road. After data acquisition and radar grams
collection, they have been processed using RadExplorer V1.4 software
implementing different filters with the most effective ones (time zero adjustment and
DC removal) in addition to other interpretation tool parameters.
The interpretatio
This study emphasizes the infinite-boundary integro-differential equation. To examine the approximate solution of the problem, two modified optimization algorithms are proposed based on generalized Laguerre functions. In the first technique, the proposed method is applied to the original problem by approximating the solution using the truncated generalized Laguerre polynomial of the unknown function, optimizing coefficients through error minimization, and transforming the integro-differential equation into an algebraic equation. In contrast, the second approach incorporates a penalty term into the objective function to effectively enforce boundary and integral constraints. This technique reduces the original problem to a mathematical optimi
... Show MoreThis paper deals with the thirteenth order differential equations linear and nonlinear in boundary value problems by using the Modified Adomian Decomposition Method (MADM), the analytical results of the equations have been obtained in terms of convergent series with easily computable components. Two numerical examples results show that this method is a promising and powerful tool for solving this problems.
Finite element method is the most widely numerical technique used in engineering field. Through the study of behavior of concrete material properties, various concrete constitutive laws and failure criteria have been developed to model the behavior of concrete. A feature of the Finite Element program (ATENA) is used in this study to model the behavior of UHPC corbel under concentrated load only. The Finite Element (FE) model is followed by verification against experimental results. Some variable effects on the shear capacity of the UHPC corbels are also demonstrated in a parametric study. A proposed design equation of shear strength of UHPC corbel was presented and checked with numerical results.
Due to wind wave actions, ships impacts, high-speed vehicles and others resources of loading, structures such as high buildings rise bridge and electric transmission towers undergo significant coupled moment loads. In this study, the effect of increasing the value of coupled moment and increasing the rigidity of raft footing on the horizontal deflection by using 3-D finite element using ABAQUS program. The results showed that the increasing the coupled moment value leads to an increase in lateral deflection and increase in the rotational angle (α◦). The rotational angle increases from (0.014, 0.15 to 0.19) at coupled moment (120 kN.m), (0.29, 0.31 and 0.49) at coupled moment (240 kN.m) and (0.57, 0.63 and 1.03) at cou
... Show MoreA progressive increase in the desire for environmentally friendly lubricants by users and strict government regulations for the use of these lubricants has provided an opportunity to use plant oils as biodegradable lubricants, therefore vegetable oils have been investigated to replace oil lubricants because of their maintaining the conditions of nature (environment) properties. In this paper, the influences of the blending ratio of mustard seeds oil with commercial mineral oil (SAE40) on the tribological characteristics were investigated and compared with mineral oil using the four-ball tribotester. Mustard seeds oil was blended with mineral oil at a volumetric ratio ranging from 22.5 to 90%. All experimental works were
... Show MoreThe study using Nonparametric methods for roubust to estimate a location and scatter it is depending minimum covariance determinant of multivariate regression model , due to the presence of outliear values and increase the sample size and presence of more than after the model regression multivariate therefore be difficult to find a median location .
It has been the use of genetic algorithm Fast – MCD – Nested Extension and compared with neural Network Back Propagation of multilayer in terms of accuracy of the results and speed in finding median location ,while the best sample to be determined by relying on less distance (Mahalanobis distance)has the stu
... Show More