History of Elasticity· Nikolay Ivanovich Muskhelisvili (1891-1976): A Soviet Georgian mathematician: Throughout his life, he solved many elasticproblems using the complex variableformulation, including 2-D plane problemsthe torsional problems, and some thermo-elastic problems.·Some basic problems ofthe mathematicaltheory of elasticity, 1963: Singular integral equations, 1946.: Provided the best method for solving practicalengineering before FEM gains popular11
• Nikolay Ivanovich Muskhelisvili (1891−1976) 11 • A Soviet Georgian mathematician • Throughout his life, he solved many elastic problems using the complex variable formulation, including 2-D plane problems, the torsional problems, and some thermoelastic problems. • Some basic problems of the mathematical theory of elasticity, 1963. • Singular integral equations, 1946. • Provided the best method for solving practical engineering before FEM gains popular. History of Elasticity
History of Elasticity? Solution to Some Important Problems in Elasticity: Sophie Germain (1776-1831): Vibrational modal shapes ofelastic thin-plates, 1816 (A 3000 francs problem); alsoadvanced Fermat's Last Theorem? Kelvin's problem: concentrated force acting in the interior of aninfinite solid, 1848: Cerruti's Problem: concentrated force acting parallel to the freesurface of a semi-infinite solid, 1882.: Boussinesq's problem: concentrated force acting normal to thefree surface of a semi-infinite solid.1885: Mindlin's problem: concentrated force acting in the interior of asemi-infinite solid, 193612
• Solution to Some Important Problems in Elasticity 12 • Sophie Germain (1776−1831): Vibrational modal shapes of elastic thin-plates, 1816 (A 3000 francs problem); also advanced Fermat’s Last Theorem. • Kelvin’s problem: concentrated force acting in the interior of an infinite solid, 1848. • Cerruti’s Problem: concentrated force acting parallel to the free surface of a semi-infinite solid, 1882. • Boussinesq’s problem: concentrated force acting normal to the free surface of a semi-infinite solid, 1885. • Mindlin’s problem: concentrated force acting in the interior of a semi-infinite solid, 1936. History of Elasticity