Engineering Analysis in Applied Mechanics
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Engineering Analysis in Applied Mechanics

Engineering Analysis in Applied Mechanics


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About the Book

Table of Contents:
Theory of equations: simultaneous equations in the mechanical sciences - equilibrium; the theory of simultaneous equations; engineering mechanics - structures in equilibrium; Eigenvalues and Eigenvectors; Eigenvalues and Eigenvectors in the mechanical sciences. Theory of the extreme values of functions: extremalization of functions - first derivative necessary and sufficient conditions; functions of more than one independent variable and stationarity; second-order necessary or sufficient conditions; the conditions for constrained extrema; engineering mathematics; inequality constraints and Kuhn-Tucker theory complementary variables and the dual program. The calculus of variations: background - functions, functionals, and variations; the "simplest problem" and the Euler-Lagrange equation; more general formulations in the calculus of variations; solutions of classic problems; a second-order necessary condition; engineering physics; differential equations as constraints; engineering economics. The extremum principles of thermodynamics; the physics of thermodynamics; postulates and extremum principles in thermodynamics; the mathematical structure of thermodynamics; Legendre transforms and extremum principles in thermodynamics; the thermodynamics of engines; Maxwell relations, reduction of derivatives, and thermodynamic stability. The stationarity and extremum principles of solid mechanics: virtual work - ideal systems of rigid bodies; elastic energy and systems of prismatic members; complementary energy and the Crotti-Engesser theorem; energy methods and deflection of continuous beams. Equations of motion and the stationarity principles of Lagrange and Hamilton: background - coordinates and kinetic energy; Lagrange's equations of motion for particles; Hamilton's canonical equations; the equations of planar motion of rigid bodies; the equations of 3-D motion of rigid bodies; on the nature of constraints - holonomic and non-holonomic. Appendixes: matrix algebra and the linear independence of vectors - matrix notation, the addition and multiplication matrices, determinants and inverses, linear independence and matrix rank, existence and uniqueness of solutions to simultaneous algebraic equations; a review of elementary real analysis - functions and limits, continuous functions, derivatives, the law of mean, functions of more than one variable, sets of functions of n variables, numerical solutions of nonlinear equations.


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Product Details
  • ISBN-13: 9789056996840
  • Publisher: Gordon and Breach
  • Publisher Imprint: Harwood Academic (Medical, Reference and Social Sc
  • Height: 230 mm
  • Returnable: N
  • ISBN-10: 9056996843
  • Publisher Date: 01 Jun 2001
  • Binding: Hardback
  • Language: English


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