TY  - BOOK
AU  - Campos,Luis Manuel Braga da Costa
TI  - Higher-order differential equations and elasticity
T2  - Mathematics and physics for science and technology
SN  - 9780367137205
U1  - 531.01 
PY  - 2020///
CY  - Boca Raton
PB  - CRC Press, Taylor & Francis Group
KW  - Elasticity
KW  - Mathematical models
KW  - Thermoelasticity
KW  - Differential equations
N1  - Includes bibliographical references and index
N2  - Higher-Order Differential Equations and Elasticity is the third book within Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume Set. As a set, they are the fourth volume in the series Mathematics and Physics Applied to Science and Technology. This third book consists of two chapters (chapters 5 and 6 of the set). The first chapter in this book concerns non-linear differential equations of the second and higher orders. It also considers special differential equations with solutions like envelopes not included in the general integral. The methods presented include special differential equations, whose solutions include the general integral and special integrals not included in the general integral for myriad constants of integration. The methods presented include dual variables and differentials, related by Legendre transforms, that have application in thermodynamics. The second chapter concerns deformations of one (two) dimensional elastic bodies that are specified by differential equations of: (i) the second-order for non-stiff bodies like elastic strings (membranes); (ii) fourth-order for stiff bodies like bars and beams (plates). The differential equations are linear for small deformations and gradients and non-linear otherwise. The deformations for beams include bending by transverse loads and buckling by axial loads. Buckling and bending couple non-linearly for plates. The deformations depend on material properties, for example isotropic or anisotropic elastic plates, with intermediate cases such as orthotropic or pseudo-isotropic
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ER  -