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  2. Moving heat source model for thin plates - Wikipedia

    en.wikipedia.org/wiki/Moving_heat_source_model...

    In the 1930s metallurgists Albert Portevin and D. Seferian attempted to experimentally determine heat transfer characteristics in welding. [1] They correlated the effects of several factors—material properties, welding process, and part dimensions—on temperature distribution, by performing oxyacetylene (gas) and covered electrode (arc) welds on plates and bars of various profiles, and ...

  3. Föppl–von Kármán equations - Wikipedia

    en.wikipedia.org/wiki/Föppl–von_Kármán...

    While the Föppl–von Kármán equations are of interest from a purely mathematical point of view, the physical validity of these equations is questionable. [7] Ciarlet [8] states: The two-dimensional von Karman equations for plates, originally proposed by von Karman [1910], play a mythical role in applied mathematics. While they have been ...

  4. Plate theory - Wikipedia

    en.wikipedia.org/wiki/Plate_theory

    In general, exact solutions for cantilever plates using plate theory are quite involved and few exact solutions can be found in the literature. Reissner and Stein [7] provide a simplified theory for cantilever plates that is an improvement over older theories such as Saint-Venant plate theory.

  5. Bending of plates - Wikipedia

    en.wikipedia.org/wiki/Bending_of_plates

    In this case we start with an assumed form of the displacement and try to fit the parameters so that the governing equation and the boundary conditions are satisfied. The goal is to find Y m ( y ) {\displaystyle Y_{m}(y)} such that it satisfies the boundary conditions at y = 0 {\displaystyle y=0} and y = b {\displaystyle y=b} and, of course ...

  6. 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: + +

  7. Energy release rate (fracture mechanics) - Wikipedia

    en.wikipedia.org/wiki/Energy_release_rate...

    In fracture mechanics, the energy release rate, , is the rate at which energy is transformed as a material undergoes fracture.Mathematically, the energy release rate is expressed as the decrease in total potential energy per increase in fracture surface area, [1] [2] and is thus expressed in terms of energy per unit area.

  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. Displacement field (mechanics) - Wikipedia

    en.wikipedia.org/wiki/Displacement_field_(mechanics)

    A displacement field is a vector field of all displacement vectors for all particles in the body, which relates the deformed configuration with the undeformed configuration. The distance between any two particles changes if and only if deformation has occurred. If displacement occurs without deformation, then it is a rigid-body displacement.