@article{946328,
      recid = {946328},
      author = {Constanda, Christian.},
      title = {The generalized Fourier series method : bending of elastic  plates /},
      publisher = {Springer,},
      address = {Cham :},
      pages = {1 online resource},
      year = {2021},
      abstract = {This book explains in detail the generalized Fourier  series technique for the approximate solution of a  mathematical model governed by a linear elliptic partial  differential equation or system with constant coefficients.  The power, sophistication, and adaptability of the method  are illustrated in application to the theory of plates with  transverse shear deformation, chosen because of its  complexity and special features. In a clear and accessible  style, the authors show how the building blocks of the  method are developed, and comment on the advantages of this  procedure over other numerical approaches. An extensive  discussion of the computational algorithms is presented,  which encompasses their structure, operation, and accuracy  in relation to several appropriately selected examples of  classical boundary value problems in both finite and  infinite domains. The systematic description of the  technique, complemented by explanations of the use of the  underlying software, will help the readers create their own  codes to find approximate solutions to other similar  models. The work is aimed at a diverse readership,  including advanced undergraduates, graduate students,  general scientific researchers, and engineers. The book  strikes a good balance between the theoretical results and  the use of appropriate numerical applications. The first  chapter gives a detailed presentation of the differential  equations of the mathematical model, and of the associated  boundary value problems with Dirichlet, Neumann, and Robin  conditions. The second chapter presents the fundamentals of  generalized Fourier series, and some appropriate techniques  for orthonormalizing a complete set of functions in a  Hilbert space. Each of the remaining six chapters deals  with one of the combinations of domain-type (interior or  exterior) and nature of the prescribed conditions on the  boundary. The appendices are designed to give insight into  some of the computational issues that arise from the use of  the numerical methods described in the book. Readers may  also want to reference the authors' other books  Mathematical Methods for Elastic Plates, ISBN:  978-1-4471-6433-3 and Boundary Integral Equation Methods  and Numerical Solutions: Thin Plates on an Elastic  Foundation, ISBN: 978-3-319-26307-6.},
      url = {http://library.usi.edu/record/946328},
      doi = {https://doi.org/10.1007/978-3-030-55849-9.},
}