LEADER 04283oam 2200517 450 001 996418198703316 005 20210505211948.0 010 $a3-030-55849-5 024 7 $a10.1007/978-3-030-55849-9 035 $a(CKB)4100000011610338 035 $a(MiAaPQ)EBC6404813 035 $a(DE-He213)978-3-030-55849-9 035 $a(PPN)252507150 035 $a(EXLCZ)994100000011610338 100 $a20210505d2020 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe generalized Fourier series method $ebending of elastic plates /$fChristian Constanda, Dale Doty 205 $a1st ed. 2020. 210 1$aCham, Switzerland :$cSpringer,$d[2020] 210 4$d©2020 215 $a1 online resource (XIII, 254 p. 186 illus., 37 illus. in color.) 225 1 $aDevelopments in Mathematics ;$vVolume 65 311 $a3-030-55848-7 327 $a1. The Mathematical Model -- 2. Generalized Fourier Series -- 3. Interior Dirichlet Problem -- 4. Interior Neumann Problem -- 5. Interior Robin Problem -- 6. Exterior Dirichlet Problem -- 7. Exterior Neumann Problem -- 8. Exterior Robin Problem -- A. Numerical Issues -- B. Numerical Integration -- C. Interior Boundary Value Problem for D[x,y] -- D. Exterior Boundary Value Problems for D^A[X,y] -- E. Numerical Integration of P[x,y] and P^A[x,y] -- References -- Index. 330 $aThis 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. 410 0$aDevelopments in mathematics ;$vVolume 65. 606 $aFourier series 606 $aMechanics 606 $aMathematical analysis 615 0$aFourier series. 615 0$aMechanics. 615 0$aMathematical analysis. 676 $a515.2433 700 $aConstanda$b Christian$057207 702 $aDoty$b Dale 801 0$bCaPaEBR 801 1$bCaPaEBR 801 2$bUtOrBLW 906 $aBOOK 912 $a996418198703316 996 $aThe generalized Fourier series method$92018982 997 $aUNISA