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  2. Single displacement reaction - Wikipedia

    en.wikipedia.org/wiki/Single_displacement_reaction

    A single-displacement reaction, also known as single replacement reaction or exchange reaction, is an archaic concept in chemistry. It describes the stoichiometry of some chemical reactions in which one element or ligand is replaced by atom or group. [1] [2] [3] It can be represented generically as:

  3. Bending of plates - Wikipedia

    en.wikipedia.org/wiki/Bending_of_plates

    For rectangular plates, Navier in 1820 introduced a simple method for finding the displacement and stress when a plate is simply supported. The idea was to express the applied load in terms of Fourier components, find the solution for a sinusoidal load (a single Fourier component), and then superimpose the Fourier components to get the solution ...

  4. Direct stiffness method - Wikipedia

    en.wikipedia.org/wiki/Direct_stiffness_method

    The material stiffness properties of these elements are then, through linear algebra, compiled into a single matrix equation which governs the behaviour of the entire idealized structure. The structure’s unknown displacements and forces can then be determined by solving this equation.

  5. Plate theory - Wikipedia

    en.wikipedia.org/wiki/Plate_theory

    Deformation of a thin plate highlighting the displacement, the mid-surface (red) and the normal to the mid-surface (blue) The Kirchhoff–Love theory is an extension of Euler–Bernoulli beam theory to thin plates.

  6. Reissner-Mindlin plate theory - Wikipedia

    en.wikipedia.org/wiki/Reissner-Mindlin_plate_theory

    The Mindlin hypothesis implies that the displacements in the plate have the form = (,) ; =, = (,)where and are the Cartesian coordinates on the mid-surface of the undeformed plate and is the coordinate for the thickness direction, , =, are the in-plane displacements of the mid-surface, is the displacement of the mid-surface in the direction, and designate the angles which the normal to the mid ...

  7. Hooke's law - Wikipedia

    en.wikipedia.org/wiki/Hooke's_law

    Hooke's law also applies when a straight steel bar or concrete beam (like the one used in buildings), supported at both ends, is bent by a weight F placed at some intermediate point. The displacement x in this case is the deviation of the beam, measured in the transversal direction, relative to its unloaded shape.

  8. Finite element method in structural mechanics - Wikipedia

    en.wikipedia.org/wiki/Finite_element_method_in...

    The equations are written only for the small domain of individual elements of the structure rather than a single equation that describes the response of the system as a whole (a continuum). The latter would result in an intractable problem, hence the utility of the finite element method.

  9. Forming limit diagram - Wikipedia

    en.wikipedia.org/wiki/Forming_limit_diagram

    Forming limit curves (FLC) for four steel sheet grades are displayed in the attached figure. All forming limit curves have essentially the same shape. A minimum of the curve exists at the intercept with the major strain axis or close thereby, the plane strain forming limit.