{"product_id":"2940148622185","title":"Differential Equations of Linear Elasticity of Homogeneous Media","description":"The transmission of forces from without to within solid medium comprises a mathematical\u003cbr\u003echallenge of utmost complexity. The sources of difficulties are as follows:\u003cbr\u003e\u003cbr\u003e1. Surface indeterminate conditions\u003cbr\u003e2. Medium indeterminate relationships\u003cbr\u003e3- Spatial indeterminate continuity\u003cbr\u003e4. Fixing and loading indeterminate conditions\u003cbr\u003e5. Inertial rotational indeterminate equilibrium\u003cbr\u003e\u003cbr\u003eSTATICS OF STRESS \u003cbr\u003eNavier’s Partial differential equations of stress \u003cbr\u003eSurface conditions for projection of stress \u003cbr\u003eCauchy’s quadratic or surface of normal stresses  \u003cbr\u003eSpherical stress tensor \u003cbr\u003eStress deviator tensor \u003cbr\u003eVanishing deviator of the first invariant of the \u003cbr\u003e\u003cbr\u003eGEOMETRY OF STRAIN \u003cbr\u003eCauchy’s equations for displacement, elongation, shear, and rotational strains \u003cbr\u003eGeneral strain tensor \u003cbr\u003eDeviator and spherical strain tensors and invariants \u003cbr\u003eCubic deviations of the third invariant of the relative strain tensor \u003cbr\u003e\u003cbr\u003eVOLUMETRIC HOOKE’S LAW \u003cbr\u003eThe three components of Hooke’s law \u003cbr\u003eElastic properties of material \u003cbr\u003eRelationships between Young’s modulus, Poisson’s ratio, and Lamé’s coefficients \u003cbr\u003eElastic potential energy \u003cbr\u003e\u003cbr\u003eLAMÉ’S EQUATIONS OF CONTINUITY \u003cbr\u003e\u003cbr\u003eELASTIC VIBRATION \u003cbr\u003eVibration of unbound surfaces \u003cbr\u003eLongitudinal vibration \u003cbr\u003eTransverse vibration \u003cbr\u003eHarmonic longitudinal vibrations \u003cbr\u003eVibration of bound surfaces \u003cbr\u003e\u003cbr\u003eTORSION, BENDING, AND SUSPENSION OF A BAR \u003cbr\u003ePure shear stress \u003cbr\u003eTorsion of a circular bar \u003cbr\u003ePure bending stress \u003cbr\u003eSuspension of a bar \u003cbr\u003e\u003cbr\u003ePLANE ELASTICITY PROBLEMS \u003cbr\u003ePlane strain approximations \u003cbr\u003eModified Hooke’s law for planar strains \u003cbr\u003ePlanar stress approximations \u003cbr\u003eHooke’s law for planar stress \u003cbr\u003eInterpretation of Maurice Lévy’s equation \u003cbr\u003ePolynomial stress function \u003cbr\u003ePure bending of cantilever \u003cbr\u003eForced bending of cantilever \u003cbr\u003eUniformly loaded beam supported at both ends \u003cbr\u003eVertically loaded triangular dam \u003cbr\u003eSeparation of variables or geometrical polynomials \u003cbr\u003eBeam with infinite span \u003cbr\u003eCylindrical tube with infinite length \u003cbr\u003eCylindrical polar radial Levy’s stress function \u003cbr\u003eLame’s circular cylindrical tube \u003cbr\u003eBending a circular ring \u003cbr\u003eFinite force applied on half plane \u003cbr\u003eFlamant Boussinesg \u003cbr\u003e\u003cbr\u003eBIHARMONIC EQUATION \u003cbr\u003eBiHarmonic equation of plane stress in polar cylindrical coordinates \u003cbr\u003eVariable separation constant \u003cbr\u003e\u003cbr\u003eTORSION OF PRISMATICAL BARS \u003cbr\u003ePrismatical Circular Cylindrical Bar \u003cbr\u003eTorsion of prismatical bars \u003cbr\u003eLudwig Prandtl’s shear stress function Fx,y \u003cbr\u003ePrismatical Elliptic Cylindrical Bar \u003cbr\u003eComplex stress and torsion functions \u003cbr\u003eTorsional angle or angle of twist \u003cbr\u003eDeformed crosssection contour \u003cbr\u003eTriangular Prismatical Bar \u003cbr\u003eComplex function representation of triangular geometry \u003cbr\u003ePrismatical bar with rectangular crosssection \u003cbr\u003eMembrane surface tension with Ludwig Prandtl’s stress function \u003cbr\u003e\u003cbr\u003e\u003cbr\u003eGENERAL SOLUTION OF ELASTICITY PROBLEMS \u003cbr\u003eBeltrami Michell Equations \u003cbr\u003eMaxwell’s stress functions \u003cbr\u003eMorera’s stress functions \u003cbr\u003ePlane stress in cylindrical coordinates \u003cbr\u003eHarmonic equation \u003cbr\u003eConcentrated load on half space medium \u003cbr\u003eDistributed load on half space medium \u003cbr\u003eFilon’s solution of plain stress problem by complex variables \u003cbr\u003eAiry stress function with complex harmonic function \u003cbr\u003eElastic vibrational waves \u003cbr\u003e\u003cbr\u003eTHIN SLAB \u003cbr\u003eSOLUTION BY PLANE APPROXIMATION \u003cbr\u003eBending of rod versus bending of thin slab \u003cbr\u003eSophie Germain’s equation for bending and torsion of thin slab \u003cbr\u003eElliptic plate \u003cbr\u003eCircular plate \u003cbr\u003eRectangular plate \u003cbr\u003eNavier’s method \u003cbr\u003eLevy’s method \u003cbr\u003e\u003cbr\u003eVARIATIONAL METHOD OF SOLUTION IN PLANAR ELASTICITY \u003cbr\u003eClapeyron’s Theorem in Linear Elasticity \u003cbr\u003eLagrange’s geometrical variation \u003cbr\u003eVibrational perturbation of displacements and strains \u003cbr\u003eElastic body energy \u003cbr\u003eVirtual work done \u003cbr\u003ePlane crosssection approximations in thick media \u003cbr\u003eLagrange’s equation for threedimensional arbitrary body \u003cbr\u003eCastigliano’s static variation \u003cbr\u003eTorsion of prismatical rod \u003cbr\u003eCastigliano’s variation equation for torsion of rod \u003cbr\u003eLaplace’s form of Castigliano’s variation equation for torsion of rod \u003cbr\u003ePractical approximate solution of elasticity by method of variation of elastic energy \u003cbr\u003eLame’s problem of rectangular prism \u003cbr\u003e","brand":"Mohamed F. El-Hewie","offers":[{"title":"Default Title","offer_id":47067951366384,"sku":"2940148622185","price":25.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/2940148622185_p0.jpg?v=1763706129","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/2940148622185","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}