LEADER 04216nam 22007215 450 001 9910299989603321 005 20220415223126.0 010 $a1-4471-6434-2 024 7 $a10.1007/978-1-4471-6434-0 035 $a(CKB)3710000000143764 035 $a(EBL)1781963 035 $a(SSID)ssj0001276612 035 $a(PQKBManifestationID)11662827 035 $a(PQKBTitleCode)TC0001276612 035 $a(PQKBWorkID)11246988 035 $a(PQKB)10009707 035 $a(MiAaPQ)EBC1781963 035 $a(DE-He213)978-1-4471-6434-0 035 $a(PPN)179766961 035 $a(EXLCZ)993710000000143764 100 $a20140624d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMathematical methods for elastic plates /$fby Christian Constanda 205 $a1st ed. 2014. 210 1$aLondon :$cSpringer London :$cImprint: Springer,$d2014. 215 $a1 online resource (213 p.) 225 1 $aSpringer Monographs in Mathematics,$x1439-7382 300 $aDescription based upon print version of record. 311 $a1-322-13230-5 311 $a1-4471-6433-4 320 $aIncludes bibliographical references and index. 327 $aSingular Kernels -- Potentials and Boundary Integral Equations -- Bending of Elastic Plates -- The Layer Potentials -- The Newtonian Potential -- Existence of Regular Solutions -- Complex Variable Treatment -- Generalized Fourier Series. 330 $aMathematical models of deformation of elastic plates are used by applied mathematicians and engineers in connection with a wide range of practical applications, from microchip production to the construction of skyscrapers and aircraft. This book employs two important analytic techniques to solve the fundamental boundary value problems for the theory of plates with transverse shear deformation, which offers a more complete picture of the physical process of bending than Kirchhoff?s classical one.   The first method transfers the ellipticity of the governing system to the boundary, leading to singular integral equations on the contour of the domain. These equations, established on the basis of the properties of suitable layer potentials, are then solved in spaces of smooth (Hölder continuous and Hölder continuously differentiable) functions.   The second technique rewrites the differential system in terms of complex variables and fully integrates it, expressing the solution as a combination of complex analytic potentials.   The last chapter develops a generalized Fourier series method closely connected with the structure of the system, which can be used to compute approximate solutions. The numerical results generated as an illustration for the interior Dirichlet problem are accompanied by remarks regarding the efficiency and accuracy of the procedure.   The presentation of the material is detailed and self-contained, making Mathematical Methods for Elastic Plates accessible to researchers and graduate students with a basic knowledge of advanced calculus. 410 0$aSpringer Monographs in Mathematics,$x1439-7382 606 $aMathematical analysis 606 $aAnalysis (Mathematics) 606 $aIntegral equations 606 $aMechanics 606 $aMechanics, Applied 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 606 $aIntegral Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12090 606 $aSolid Mechanics$3https://scigraph.springernature.com/ontologies/product-market-codes/T15010 615 0$aMathematical analysis. 615 0$aAnalysis (Mathematics). 615 0$aIntegral equations. 615 0$aMechanics. 615 0$aMechanics, Applied. 615 14$aAnalysis. 615 24$aIntegral Equations. 615 24$aSolid Mechanics. 676 $a531.382 700 $aConstanda$b Christian$4aut$4http://id.loc.gov/vocabulary/relators/aut$057207 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299989603321 996 $aMathematical methods for elastic plates$91410652 997 $aUNINA