LEADER 05844nam 2200721Ia 450 001 9910782387303321 005 20230607222141.0 010 $a1-281-93450-X 010 $a9786611934507 010 $a981-279-456-5 035 $a(CKB)1000000000537975 035 $a(EBL)1679607 035 $a(SSID)ssj0000107018 035 $a(PQKBManifestationID)11137928 035 $a(PQKBTitleCode)TC0000107018 035 $a(PQKBWorkID)10007002 035 $a(PQKB)11558681 035 $a(MiAaPQ)EBC1679607 035 $a(WSP)00004790 035 $a(Au-PeEL)EBL1679607 035 $a(CaPaEBR)ebr10255465 035 $a(CaONFJC)MIL193450 035 $a(OCoLC)879074218 035 $a(EXLCZ)991000000000537975 100 $a20020116d2001 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAsymptotic methods in the buckling theory of elastic shells$b[electronic resource] /$fPetr E. Tovstik, Andrei L. Smirnov ; edited by Peter R. Frise, Ardeshir Guran 210 $aSingapore ;$aRiver Edge, N.J. $cWorld Scientific$d2001 215 $a1 online resource (360 p.) 225 1 $aSeries on stability, vibration, and control of systems. Series A ;$vv. 4 300 $aDescription based upon print version of record. 311 $a981-02-4726-5 320 $aIncludes bibliographical references (p. 321-334) and index. 327 $aPreface; Contents; Introduction; Basic notation; 1 Equations of Thin Elastic Shell Theory; 1.1 Elements of Surface Theory; 1.2 Equilibrium Equations and Boundary Conditions; 1.3 Errors of 2D Shell Theory of Kirchhoff-Love Type; 1.4 Membrane Stress State; 1.5 Technical Shell Theory Equations; 1.6 Technical Theory Equations in the Other Cases; 1.7 Shallow Shells; 1.8 Initial Imperfections; 1.9 Cylindrical Shells; 1.10 The Potential Energy of Shell Deformation; 1.11 Problems and Exercises; 2 Basic Equations of Shell Buckling; 2.1 Types of Elastic Shell Buckling; 2.2 The Buckling Equations 327 $a2.3 The Buckling Equations for a Membrane State2.4 Buckling Equations of the General Stress State; 2.5 Problems and Exercises; 3 Simple Buckling Problems; 3.1 Buckling of a Shallow Convex Shell; 3.2 Shallow Shell Buckling Modes; 3.3 The Non-Uniqueness of Buckling Modes; 3.4 A Circular Cylindrical Shell Under Axial Compression; 3.5 A Circular Cylindrical Shell Under External Pressure; 3.6 Estimates of Critical Load; 3.7 Problems and Examples; 4 Buckling Modes Localized near Parallels; 4.1 Local Shell Buckling Modes; 4.2 Construction Algorithm of Buckling Modes 327 $a4.3 Buckling Modes of Convex Shells of Revolution4.4 Buckling of Shells of Revolution Without Torsion; 4.5 Buckling of Shells of Revolution Under Torsion; 4.6 Problems and Exercises; 5 Non-homogeneous Axial Compression of Cylindrical Shells; 5.1 Buckling Modes Localized near Generatrix; 5.2 Reconstruction of the Asymptotic Expansions; 5.3 Axial Compression and Bending of Cylindrical Shell; 5.4 The Influence of Internal Pressure; 5.5 Buckling of a Non-Circular Cylindrical Shell; 5.6 Cylindrical Shell with Curvature of Variable Sign; 5.7 Problems and Exercises 327 $a6 Buckling Modes Localized at a Point6.1 Local Buckling of Convex Shells; 6.2 Construction of the Buckling Mode; 6.3 Ellipsoid of Revolution Under Combined Load; 6.4 Cylindrical Shell Under Axial Compression; 6.5 Construction of the Buckling Modes; 6.6 Problems and Exercises; 7 Semi-momentless Buckling Modes; 7.1 Basic Equations and Boundary Conditions; 7.2 Buckling Modes for a Conic Shell; 7.3 Effect of Initial Membrane Stress Resultants; 7.4 Semi-Momentless Buckling Modes of Cylindrical Shells; 7.5 Problems and Exercises; 8 Effect of Boundary Conditions on Semi-momentless Modes 327 $a8.1 Construction Algorithm for Semi-Momentless Solutions8.2 Semi-Momentless Solutions; 8.3 Edge Effect Solutions; 8.4 Separation of Boundary Conditions; 8.5 The Effect of Boundary Conditions on the Critical Load; 8.6 Boundary Conditions and Buckling of a Cylindrical Shell; 8.7 Conic Shells Under External Pressure; 8.8 Problems and Exercises; 9 Torsion and Bending of Cylindrical and Conic Shells; 9.1 Torsion of Cylindrical Shells; 9.2 Cylindrical Shell under Combined Loading; 9.3 A Shell with Non-Constant Parameters Under Torsion; 9.4 Bending of a Cylindrical Shell 327 $a9.5 The Torsion and Bending of a Conic Shell 330 $aThis book contains solutions to the most typical problems of thin elastic shells buckling under conservative loads. The linear problems of bifurcation of shell equilibrium are considered using a two-dimensional theory of the Kirchhoff-Love type. The explicit approximate formulas obtained by means of the asymptotic method permit one to estimate the critical loads and find the buckling modes. The solutions to some of the buckling problems are obtained for the first time in the form of explicit formulas. Special attention is devoted to the study of the shells of negative Gaussian curvature, the b 410 0$aSeries on stability, vibration, and control of systems.$nSeries A ;$vv. 4. 606 $aShells (Engineering) 606 $aAsymptotic expansions 606 $aDifferential equations$xAsymptotic theory 615 0$aShells (Engineering) 615 0$aAsymptotic expansions. 615 0$aDifferential equations$xAsymptotic theory. 676 $a624.17762 700 $aTovstik$b P. E$01489392 701 $aSmirnov$b Andrei L.$f1956-$042316 701 $aFrise$b Peter Richard$f1958-$01489393 701 $aGuran$b A$g(Arde?shir)$01083500 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910782387303321 996 $aAsymptotic methods in the buckling theory of elastic shells$93710079 997 $aUNINA