Analytical solution for beams with multipoint boundary conditions on two-parameter elastic foundations

Analysis of a Nonlinear ψ-Hilfer Fractional Integro-Differential Equation Describing Cantilever Beam Model with Nonlinear Boundary Conditions

“…Proof. We transform the ψ-Hilfer FBVP describing the CB model ( 4) into x = T x, where T is defined by (12). Clearly, the fixed points of T are the possible solutions of the ψ-Hilfer FBVP describing the CB model ( 4).…”

Combined application of finite element method and discrete-continual finite element method

“…Combined (mixed) application of finite element method (FEM) [1,2] and DCFEM [3][4][5][6]7,8] can be effectively used for the analysis of general and complex structures. Some potentially dangerous areas of structure can be taken into account within DCFEM, and no special attention shall paid to compatibility method or time required to solve the corresponding mathematical problem, as the rest part of the structure which presents no interest in terms of fracture is considered by standard FEM.…”

“…The right subdomain is approximated by finite elements (within FEM [1,2,[11][12][13][14][15][16][17][18]) and the left subdomain is approximated by discrete-continual finite elements (within DCFEM [3][4][5][6]7,8]). Elasticity modulus of material of structure is equal to 3000 E kN/cm 2 .…”

“…Akimov and A.B. Zolotov [3][4][5][6]. But, as shown above, DCFEM is useful only for limited variety of constructions.…”

“…But, as shown above, DCFEM is useful only for limited variety of constructions. Combined (mixed) application of finite element method (FEM) [1,2] and DCFEM [3][4][5][6]7,8] is apparently preferable using the most powerful advantages of these methods and avoiding their disadvantages. The paper is devoted to such approach of semianalytical structural analysis.…”