İnşaat Mühendisliği Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/395
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Article Orthonormal decomposition of symmetric second rank tensors(2010) Dinçkal, ÇiğdemIn this paper, a new orthonormal decomposition method for symmetric second rank tensors namely as, orthonormal tensor basis is presented. Complex variable representation method is developed by using the existing theories in literature. For comparison purposes, a brief review of the spectral method is given. It is shown that stress tensor, as an example to symmetric second rank tensors, is decomposed into six orthonormal parts by orthonormal tensor basis and complex variable representation methods. The matrix forms of these decomposed parts are given. This is the first time in literature that physical meanings of each six decomposed parts which are obtained from the orthonormal decomposition of stress tensor by orthonormal tensor basis and complex variable representation methods, different from the traditionally form, are emphasized. Illustrative applications on orthonormal tensor basis and complex variable representation decomposition methods are given. Finally, it is proved that the spectral method is a non-linear decomposition method which yields three non-linear orthonormal decomposed parts. This case is a significant innovation in decomposition procedures for symmetric second rank tensors in literature.Article Norm, norm ratio calculations and anisotropy degree(2011) Dinçkal, ÇiğdemIn this paper, for elastic constant tensor, the norm concept, norm ratio and anisotropy degree are described. The norm of a tensor is used as a criterion for comparing the overall effect of the properties of anisotropic materials and norm ratios are used as a criterion to represent the anisotropy degree of the properties of these materials. Norm and norm ratios as well as the measure of "nearness" to the nearest isotropic tensor are computed for several examples from various anisotropic materials possessing elastic symmetries such as cubic, transversely isotropic, tetragonal, trigonal and orthorhombic. These computations are used to compare and assess the anisotropy in various anisotropic materials by means of strength or magnitude and also determine the "nearness" of the nearest isotropic tensor for the materials with lower symmetry types.Article Studies on the Optimum Mechanical Response of Anısotropıc Materials Related to Elastıc Constants(2011) Dinçkal, ÇiğdemIn this paper, mechanical and elastic behaviour of anisotropic materials are investigated in order to understand the optimum mechanical behaviour of them in selected directions. For an anisotropic material with known elastic constants, it is possible to choose the best set of elastic constants (effective elastic constants) which determine the optimum mechanical and elastic properties of it. For this reason, bounds on the anisotropic elastic constants have been constructed symbollicaly for all anisotropic elastic symmetries. As illustrative examples, materials from different symmetries are selected and their elastic constants are used to compute bounds on the anisotropic elastic constants. Finally, by examining numerical results of bounds given in tables, it is seen that the materials selected from the same symmetry type which have larger interval between the bounds, are more anisotropic, whereas some materials which have smaller interval between the bounds, are closer to isotropy. The construction of bounds on anisotropic elastic constants is a significant and critical case in design of any engineering and structural materials.Article Initial value problems spreadsheet solver using VBA for engineering education(2018) Dinçkal, ÇiğdemSpreadsheet solver using VBA programming has been designed for solving initial value problems (IVPs), analytically and numerically by all Runge-Kutta (RK) methods including also fifth order with calculation of true percent relative error for corresponding RK method. This solver is user-friendly especially for beginner users of Excel and VBA.Article Analysis of Elastic Anisotropy of Wood Material for Engineering Applications(2011) Dinçkal, ÇiğdemThis paper presents a convenient method to describe the degree of the elastic anisotropy in a given type of wood and then discusses its practical values. Besides mechanical and elastic behaviour of wood are investigated in order to understand the optimum mechanical behaviour of it in selected directions. Bounds on the wood elastic constants have been constructed in terms of elasticity and compliance tensors for any type of woods by developing Hill (1952) approach. So for any type of wood with known elastic constants, it is possible to choose the best set of elastic constants (effective elastic constants) which determine the optimum mechanical and elastic properties of it. Bounds on the wood elastic constants as well as the degree of elastic anisotropy are significant and critical cases in design of any engineering and structural materials made up of wood.Book Part Harmonic Decomposition of Elastic Constant Tensor and Crystal Symmetry(2014) Dinçkal, ÇiğdemThis paper presents a new outlook on harmonic decomposition method for elastic constant tensor. Harmonic decomposition method is developed in such a way that it is applied to anisotropic engineering materials exhibiting different crystal symmetry. The explicit results for each crystal symmetry types are presented. Numerical examples serve to illustrate and verify the developed method. This new representation of elastic constant tensor is compared with other theories such as orthogonal and non-orthogonal irreducible decompositions in literature. The results demonstrate that there are significant relationships between harmonic, non-orthogonal irreducible and orthogonal irreducible decomposition methods. While in harmonic and non-orthogonal irreducible decomposition methods, decomposition of total scalar part is not orthogonal. It is proposed that it is possible to make these parts orthogonal to each other.Article Adaptation of generalized Hill inequalities to anisotropic elastic symmetries(2011) Dinçkal, ÇiğdemMechanical and elastic behaviors of anisotropic materials are investigated in an innovative way. This is based on generalized Hill inequalities. From different type of anisotropic elastic symmetries, numerical examples are given. Constructing bounds on effective eigenvalues provides a deeper understanding about mechanical behavior of anisotropic materials. Generalized Hill inequalities are adapted to all anisotropic elastic symmetries. The materials selected from the same symmetry type which have larger interval between the bounds, are more anisotropic whereas smaller interval between the bounds, are closer to isotropy. Besides it is proved that there are relations between bulk and shear modulus and eigenvalues of cubic and isotropic symmetry and by these relations, two linear invariants are found out.Article Novel Alternative Methods to Romberg Integration and Richardson’s Extrapolation with Matlab Package:Integral_Calculator(2020) Dinçkal, ÇiğdemThis paper introduces new integration methods for numerical integration problems in science and engineering applications. It is shown that the exact results of these integrals can be obtained by these methods with the use of only 2 segments. So no additional function and integrand evaluations are required for different levels of computation. This situation overcomes the computational inefficiency. A new Matlab Package; Integral_Calculator is presented. Integral_Calculator provides a user-friendly computational platform which requires only 3 data entries from the user and performs the integration and give the results for any functions to be integrated. This package has been tested for each numerical example considered below.Publication On the properties of piezoelectric materials based upon orthonormal representations(CRC Press-Taylor, 2013) Dinçkal, ÇiğdemFor piezoelectric tensor, the decomposition method based upon irreducible orthogonal representation is overviewed. Besides, orthonormal tensor basis method is improved to express any third rank tensors such as piezoelectric tensor showing the piezoelectric effect of the material properties on the structures. Numerical examples for materials from different crystal symmetry classes serve to illustrate and verify the orthonormal tensor basis method. The differences and similarities are stated by comparing the methods presented in this work and the others in literature. It is also demonstrated that for hexagonal symmetry, each decomposed parts obtained from orthonormal tensor basis method has physical meaning. Furthermore, the norm based upon orthonormal tensor basis representation of piezoelectric tensor is obtained explicitly for each crystal symmetry classes and those results are used to study the piezoelectric effect of different materials. It is also shown that one can determine in which material the piezoelectric effect is stronger by using the norm concept for any material from various crystal symmetry classes.Article Lecture Notes in Engineering and Computer Science(Newswood Limited, 2012) Dinçkal, ÇiğdemA new procedure for representation of elastic constant tensor in terms of its orthonormal decomposed parts is presented. Form invariants and orthonormalized basis elements are used to generate this decomposition method. Numerical examples from various engineering materials serve to illustrate and verify the decomposition procedure. The norm concept of elastic constant tensor and norm ratios are used to study the anisotropy of these materials. It is shown that this method allows to investigate the elastic and mechanical properties of an anisotropic material possessing any material symmetry and determine anisotropy degree of that material. For a material given from an unknown symmetry, it is possible to determine its material symmetry type by this method.