SGER: Stochastic and Convex Finite Element Methods Asociated with Micromechanics

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9910195Novel finite element method is developed for stochastic structures, i.e. those involving random elastic and/or geometric properties and subjected to random or unknown-but-bounded loads. The method is based on micromechanics. Existing literature covers well the cases when the coefficient of variation of involved random parameters, functions of fields are small, as well when the stochastic fields are defined phenomenologically. The experimental evidence necessitates for generalization of existing techniques for the case of moderate or large coefficients of variation. The only procedure existing today to tackle these problems is the Monte Carlo Method. Here, some effective numerical methods will be developed that do not necessitate the use of the Monte Carlo Method. Novel variational principles are established to deal with shear beams, bending of beams and plates, deformation of shells. The developed techniques constitute useful and efficient numerical techniques for both small, moderate or large variation of stochastic parameters, in conjunction with them being based on micro-mechanics. In addition, for the first time, the convex finite elements will be developed for problems where probabilistic information is unavailable.