Issue 46

I. Shardakov et alii, Frattura ed Integrità Strutturale, 46 (2018) 383-390; DOI: 10.3221/IGF-ESIS.46.35 385 Physical relations:     2 E 2 E 1 2 1 2 G I G I                               (2) Geometrical relations:     T    U U (3) Boundary conditions:       , / , F t F t mW t S x S        n n 0, / S S      n x (4) Initial conditions for t = 0: 0, / 0 U dU dt   (5) Here: c r V V V   is the total volume of the structure, consisting of the volumes Vc and Vr , occupied by concrete and steel reinforcement;  ,  ,   , Е are, the tensors of stresses, strain, strain rates and a unit tensor, respectively;     , I I    are the first invariants of the strain tensor and of the strain rate tensor; x is radius vector of a point in the Cartesian coordinate system; U is the displacement vector; n is the unit vector oriented along the outward normal to the surface S of the structure; S  is the surface, to which an external impulse force is applied along its normal; ρ is the material density, F ( t ) is a scalar that determines the time variation of the force impulse; m is the striker mass, W ( t ) (scalar) is the striker acceleration in the interval of striker contact with the surface of the structure (this value is recorded experimentally by an accelerometer mounted on the striker); (  ,  ) denote vector and scalar products;  is the nabla operator; G is the shear modulus,  is the Poisson's ratio; β is the parameter characterizing the dissipative properties of concrete. At c x V  the values of ρ, G,  , β correspond to the physical properties of concrete, and at r x V  they correspond to the physical properties of steel reinforcement. Figure 2: The finite element model of RC structure: (a) – a fragment of the column; (b) – reinforcement of the joint of the column, slab and cross beams; (c) – assembled structure; (d) – slab fragment; (e) – beam fragment. The numerical implementation of the mathematical model is carried out by the finite element method using ANSYS software. Fig. 2 shows the finite element mesh of the model structure (the number of nodes is 506569). It represents the main components of the structure (columns, crossbars and slabs) and their reinforcement schemes. The characteristic geometric parameters of the model structure and the physical properties of the materials are given below. (a) (b) (c) (d) (e)