Fomin V. Nonlinear dynamic design models of concrete frame buildings and structures, taking into account the plasticity of materials

Object of research - reinforced concrete frame buildings and structures under dynamic influences; goal ─ construction of the design dynamic models of the stress-strain state of reinforced concrete frame structures taking into account geometric nonlinearity of structures and physical nonlinearity and plastic properties of materials; methods ─ construction of nonlinear differential equations for solving quasistatic and dynamic bending problems for elements of reinforced concrete frame structures taking into account physical and geometric nonlinearities and plastic properties of materials on the basis of the theory of finite deformations, deformation theory of plasticity and the method of small parameter; application of Mises theory of plastic flow with strengthening for construction differential equations of deflection increments of reinforced concrete frame building elements; application of these equations for construction of boundary element method in design of reinforced concrete frame buildings using the Newmark linear acceleration method while solving dynamic problems; results ─ construction of a small parameter method for solving nonlinear elastoplastic quasi-static and dynamic problems for one-dimensional models of reinforced concrete frame buildings; development of the method of differential equation construction of nonlinear elastoplastic bending for flat models of reinforced concrete frame buildings using the theory of plastic flow by R. Mises; carrying out further development of the boundary element method for solving nonlinear elastoplastic problems for statics and dynamics of multi-storey multi-span frame buildings; development of the method of differential equation construction for spatial elastoplastic bending of elements of reinforced concrete frame buildings and structures; development of the boundary element method for investigation of spatial static and dynamic nonlinear elastoplastic problems for reinforced concrete frame buildings; implemented ─ to the design practice of NSIBC (Kyiv), LLC "Stalproekt-AB" (Odessa) and NDC "EkoBud" (Odessa) for calculating frame structure strength under seismic influence, as well as in the educational process of Odessa State Academy of Construction and Architecture for masters in disciplines "Construction Mechanics" and "Reinforced Concrete Structures"