Micro-macro investigations on the mechanical behavior and material failure using the framework of extended finite element method (XFEM)

The current dissertation provides developments on mechanical behavior and material failure modeling utilizing the framework of extended finite element method (XFEM). Different types of materials, i.e., brittle and ductile were numerically investigated at different length scales. Plain epoxy resin representing the brittle behavior was prepared and tested using digital image correlation (DIC) displacement measurement system on an Instron© load-frame under different types of loading. Advanced technology methods such as optical and scan electron microscopy (SEM) were used to characterize the failure mechanisms of the tested specimens. Also, computed tomography (CT) scans were used to identify the void content within the epoxy specimens. In addition, fracture surfaces were also CT scanned to further investigate epoxy’s failure mechanism closely. On the other hand, relevant reported testing results in the literature regarding low and high strength steel materials were used to represent the ductile behavior. Different micromechanical methods such as unit cell (UC) and representative volume element (RVE) were employed in the framework of finite element method (FEM) or XFEM to numerically obtain mechanical behaviors and/or investigate material damage from a microscopic point of view. Several algorithms were developed to automate micromechanical modeling in Abaqus, and they were implemented using Python scripting. Also, different user-defined subroutines regarding the material behavior and damage were developed for macroscopic modeling and implemented using Fortran. A chief contribution of the current dissertation is the extended Ramberg-Osgood (ERO) relationship to account for metal porosity which was enabled by utilizing micromechanical modeling along with regression analyses

OPTIMIZATION OF ALKALINE Α-AMYLASE PRODUCTION BY THERMOPHILIC BACILLUS SUBTILIS

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OPTIMIZATION OF ALKALINE Α-AMYLASE PRODUCTION BY THERMOPHILIC BACILLUS SUBTILIS

Background: Starch‐degrading amylase enzyme is important in biotechnological applications as food, fermentation, textile, paper and pharmaceutical purposes. The aim of current study to isolate alkaline thermostable α-amylase bacteria and then study the composition of medium and culture conditions to optimize cells growth and a-amylase production. Materials and Methods: Thermophilic amylase producing bacterium was isolated from local hot water-springs in Gazan city Saudi Arabia. Results: Phylogenetic analysis of 16 S rRNA sequence for the strain revealed that the strain have the same sequence of Bacillus subtilis. Maximum amylase production was observed, when B. subtilis cultured in medium containing starch at concentration 0.5%, and 10 g/L peptones as nitrogen source at pH 8.5 in when it was incubated for 48 h at 45°C. Conclusion: An amylase-producing bacterium were isolated from hot-spring water and was identified as B. subtilis. Amylase produced from B.subtilis had optimum temperature 45°C and pH 8.5 in shaking media

Spectral Collocation Approach via Normalized Shifted Jacobi Polynomials for the Nonlinear Lane-Emden Equation with Fractal-Fractional Derivative

Herein, we adduce, analyze, and come up with spectral collocation procedures to iron out a specific class of nonlinear singular Lane–Emden (LE) equations with generalized Caputo derivatives that appear in the study of astronomical objects. The offered solution is approximated as a truncated series of the normalized shifted Jacobi polynomials under the assumption that the exact solution is an element in L2. The spectral collocation method is used as a solver to obtain the unknown expansion coefficients. The Jacobi roots are used as collocation nodes. Our solutions can easily be a generalization of the solutions of the classical LE equation, by obtaining a numerical solution based on new parameters, by fixing these parameters to the classical case, we obtain the solution of the classical equation. We provide a meticulous convergence analysis and demonstrate rapid convergence of the truncation error concerning the number of retained modes. Numerical examples show the effectiveness and applicability of the method. The primary benefits of the suggested approach are that we significantly reduce the complexity of the underlying differential equation by solving a nonlinear system of algebraic equations that can be done quickly and accurately using Newton’s method and vanishing initial guesses

Explicit Chebyshev Petrov–Galerkin scheme for time-fractional fourth-order uniform Euler–Bernoulli pinned–pinned beam equation

In this research, a compact combination of Chebyshev polynomials is created and used as a spatial basis for the time fractional fourth-order Euler–Bernoulli pinned–pinned beam. The method is based on applying the Petrov–Galerkin procedure to discretize the differential problem into a system of linear algebraic equations with unknown expansion coefficients. Using the efficient Gaussian elimination procedure, we solve the obtained system of equations with matrices of a particular pattern. The L∞{L}_{\infty } and L2{L}_{2} norms estimate the error bound. Three numerical examples were exhibited to verify the theoretical analysis and efficiency of the newly developed algorithm

A Fast Galerkin Approach for Solving the Fractional Rayleigh–Stokes Problem via Sixth-Kind Chebyshev Polynomials

Herein, a spectral Galerkin method for solving the fractional Rayleigh–Stokes problem involving a nonlinear source term is analyzed. Two kinds of basis functions that are related to the shifted sixth-kind Chebyshev polynomials are selected and utilized in the numerical treatment of the problem. Some specific integer and fractional derivative formulas are used to introduce our proposed numerical algorithm. Moreover, the stability and convergence accuracy are derived in detail. As a final validation of our theoretical results, we present a few numerical examples

Eighth-Kind Chebyshev Polynomials Collocation Algorithm for the Nonlinear Time-Fractional Generalized Kawahara Equation

In this study, we present an innovative approach involving a spectral collocation algorithm to effectively obtain numerical solutions of the nonlinear time-fractional generalized Kawahara equation (NTFGKE). We introduce a new set of orthogonal polynomials (OPs) referred to as “Eighth-kind Chebyshev polynomials (CPs)”. These polynomials are special kinds of generalized Gegenbauer polynomials. To achieve the proposed numerical approximations, we first derive some new theoretical results for eighth-kind CPs, and after that, we employ the spectral collocation technique and incorporate the shifted eighth-kind CPs as fundamental functions. This method facilitates the transformation of the equation and its inherent conditions into a set of nonlinear algebraic equations. By harnessing Newton’s method, we obtain the necessary semi-analytical solutions. Rigorous analysis is dedicated to evaluating convergence and errors. The effectiveness and reliability of our approach are validated through a series of numerical experiments accompanied by comparative assessments. By undertaking these steps, we seek to communicate our findings comprehensively while ensuring the method’s applicability and precision are demonstrated

Modal Shifted Fifth-Kind Chebyshev Tau Integral Approach for Solving Heat Conduction Equation

In this study, a spectral tau solution to the heat conduction equation is introduced. As basis functions, the orthogonal polynomials, namely, the shifted fifth-kind Chebyshev polynomials (5CPs), are used. The proposed method’s derivation is based on solving the integral equation that corresponds to the original problem. The tau approach and some theoretical findings serve to transform the problem with its underlying conditions into a suitable system of equations that can be successfully solved by the Gaussian elimination method. For the applicability and precision of our suggested algorithm, some numerical examples are given