Shell structures are extremely safe structures as well as being very advantageous economically in terms of materials due to their extremely small thickness compared to other dimensions, the suitability of the system geometries to transform the stress distribution into compressive stresses, and the minimization of bending effects. Although construction technologies and material properties have changed, they have been preferred for centuries in terms of aesthetics. They are also preferred in terms of being able to pass and/or cover large areas safely. Beyond commonly encountered geometries such as domes, cross vaults, hyperbolic paraboloids, and cylinders, these structures can be designed with diverse geometric features to align with aesthetic and functional requirements. The most prevalent geometric shapes are combinations of spherical dome, cylindrical wall, circular plate, and circular beam elements.

Shell structures, frequently employed in structures of significance in terms of construction and function, are among the mathematically and geometrically complex structural systems in terms of exact solution. This situation causes various assumptions to be made in the solution of the mathematical expressions of shell structures or alternative solution methods to be researched. Nowadays, computer programs based on finite element and sometimes finite difference formulations are preferred for the analysis of such structures. However, in the analyses performed with these methods, problems such as the excessive number of unknowns and computational volume, difficulties in the mathematical model preparation phase, the inability of the results to provide the necessary and sufficient details for design, and the impracticality of optimization are experienced.

Within the scope of the present book, the importance of the classical shell (flexibility) method, which is accepted as the exact solution method for the analysis of axisymmetric shell structures, is emphasized. In the analysis of axisymmetric walls that do not have sufficient height (Short Wall), although the analytical formula produces a more accurate and faster solution compared to the Finite Element method, it may sometimes be insufficient for the exact solution. In the literature, the analytical solution can be achieved with only two integral constants. In the present book, this method is described as the "two unknown" formulation of the axial wall. In order to obtain the exact solution of the analytical formula, an additional method is described which gives exact solution analysis results for the axisymmetric wall formulation with four unknowns. The method was described by Prof. Dr. Ergin Çıtıpıtıoğlu (Note: A respectful acknowledgment is extended to our esteemed professor who has made great contributions to the benefit of humanity and the World of Science). The algorithm as well as the formulation of the method was prepared by Prof. Dr. Namık Kemal ÖZTORUN, one of the authors of the present book, and the requisite computer programs were developed on this formulation. In this book, the method is defined as the "four unknown" formulation of the axial wall, demonstrating its efficacy in providing exact solution results, even for short walls.

Computer programs have been utilized on different platforms and computers over various periods, resulting in numerous versions of the developed programs. First, a Fortran-4 version was prepared for multi-user computers. Subsequently, there arose a need to adapt the program for single-user computers (PC). However, due to the prolonged unavailability of the necessary hardware to run multi-user Fortran compilers on single-user computers, the program code was initially transformed into Interpreter Basic (non-compiler, converter) and later into Compiler Basic versions. Due to challenges encountered in Interpreter Basic and Compiler Basic programs, the code was successively converted to Pascal, C++, and finally Java compilers. After the Millennium Fortran compilers became available for single-user computers, the program was adapted to the Fortran compiler again by Öztorun N., K. and Öztorun E., the authors of the present book [19]. Given the standardization of the Fortran compiler, it is possible to obtain executable program files from Fortran software using the existing program code.

Within the scope of the book, Chapter 13 provides techniques for preparing analysis models using the Finite Element Method to obtain analysis results as accurate as possible for axisymmetric shell structures. The described techniques focus on defining axial symmetric behavior under boundary conditions and enable the preparation of a much more detailed model on a small slice of the structural system. With the assistance of these techniques, it becomes possible to create a more detailed mathematical model with fewer unknowns and obtain more detailed analysis results.

In the following chapters of the book, Chapter 3 presents real-life photographs and figures along with the application stages of a concrete shell structure. Chapter 4 provides a general formulation for shell structures using classical shell theory. The analysis method and macro flowchart for defining the axial symmetric wall with two unknowns are sequentially explained in Chapters 10 and 11, while the analysis method and macro flowchart for defining the axial symmetric wall with four unknowns are detailed in Chapters 5 and 12. The computer program developed based on the two-unknown formulation, ESKA-2 (Eksenel Simetrik Kabuk Analizi - 2 in Turkish language) along with analysis examples, is presented in Chapter 14. Similarly, the computer program developed based on the four-unknown formulation, ESKA-4 (Eksenel Simetrik Kabuk Analizi – 4 in Turkish language) and its analysis examples are provided in Chapter 15. The essential formulas to be used are presented in Chapter 10 and the comparison of the results of Finite Element, ESKA-2 and ESKA-4 analyses with the examples are discussed in Chapter 13.

As preliminary information, a solid understanding of subjects such as Statics, Strength of Materials, Elasticity, Energy Principles, and similar concepts would be highly beneficial for a more extensive comprehension of the current book. To establish the basis for the shell structure formulation, the Force Method, and a detailed understanding of the static classification of structural systems, it is recommended to refer to the book "Structural Analysis II," also authored by the same writers. This will enhance the reader's ability to follow and grasp the content of the present book more comfortably.

Kind Regards to the World of Science.

Prof. Dr. Namık Kemal ÖZTORUN
Dr. Ezgi ÖZTORUN KÖROĞLU