Stiffness estimation and equivalence of boundary conditions in FEM models

The paper deals with methods of equivalence of boundary conditions in finite element models that are based on finite element model updating technique. The proposed methods are based on the determination of the stiffness parameters in the section plate or region, where the boundary condition or the removed part of the model is replaced by the bushing connector. Two methods for determining its elastic properties are described. In the first case, the stiffness coefficients are determined by a series of static finite element analyses that are used to obtain the response of the removed part to the six basic types of loads. The second method is a combination of experimental and numerical approaches. The natural frequencies obtained by the measurement are used in finite element (FE) optimization, in which the response of the model is tuned by changing the stiffness coefficients of the bushing. Both methods provide a good estimate of the stiffness at the region where the model is replaced by an equivalent boundary condition. This increases the accuracy of the numerical model and also saves computational time and capacity due to element reduction.Web of Science114art. no. 148

Analysis of stress and deformation fields of shape complex beams

In this paper is investigated the analysis of stress and deformation fields of shape complex beams. The shape complex beams are made from load-bearing sheet (trapezoidal sheet) circumferentially connected with strips of sheet metal, these beams are a substitute for more complex and heavier beams. The numerical analysis with static load are performed for these beams. The effect of three different types of connections between load-bearing sheet and strips of sheet metal is investigated. The first type of connection is represented by the trapezoidal sheet perfectly welded to the strips of sheet metal, the second type of connection is represented by the trapezoidal sheet welded to the strips of sheet metal only on the base sides of the trapezoidal sheet. The third one is represented by point welds. The stress and deformation fields for all types of the connections are compared and the suitable variant is chosen

Analysis of stress and deformation fields of shape complex beams

In this paper is investigated the analysis of stress and deformation fields of shape complex beams. The shape complex beams are made from load-bearing sheet (trapezoidal sheet) circumferentially connected with strips of sheet metal, these beams are a substitute for more complex and heavier beams. The numerical analysis with static load are performed for these beams. The effect of three different types of connections between load-bearing sheet and strips of sheet metal is investigated. The first type of connection is represented by the trapezoidal sheet perfectly welded to the strips of sheet metal, the second type of connection is represented by the trapezoidal sheet welded to the strips of sheet metal only on the base sides of the trapezoidal sheet. The third one is represented by point welds. The stress and deformation fields for all types of the connections are compared and the suitable variant is chosen

Buckling analysis of graphene nanosheets by the finite element method

The paper is devoted to the problems related to buckling analysis of graphene sheets without and with vacancies in the structure under different boundary conditions. The analysis was performed by the classical numerical treatment – the finite element method (FEM). The graphene sheets were modelled by beam elements. Interatomic relations between carbon atoms in the structure were represented by the beams connecting individual atoms. The behaviour of the beam as structural element was based on the properties that were established from relations of molecular mechanics. The vacancies in single layer graphene sheets (SLGSs) were created by elimination of randomly chosen atoms and corresponding beam elements connected to the atoms in question. The computations were accomplished for different percentage of atom vacancies and the results represent an obvious fact that the critical buckling force decreases for increased percentage of vacancies in the structure. The numerical results are represented in form of graphs

Buckling analysis of graphene nanosheets by the finite element method

The paper is devoted to the problems related to buckling analysis of graphene sheets without and with vacancies in the structure under different boundary conditions. The analysis was performed by the classical numerical treatment – the finite element method (FEM). The graphene sheets were modelled by beam elements. Interatomic relations between carbon atoms in the structure were represented by the beams connecting individual atoms. The behaviour of the beam as structural element was based on the properties that were established from relations of molecular mechanics. The vacancies in single layer graphene sheets (SLGSs) were created by elimination of randomly chosen atoms and corresponding beam elements connected to the atoms in question. The computations were accomplished for different percentage of atom vacancies and the results represent an obvious fact that the critical buckling force decreases for increased percentage of vacancies in the structure. The numerical results are represented in form of graphs

Design and strength analysis of C-hook for load using the finite element method

The special type of C-hook is investigated in this paper. The C-hook is designed to carry a special load, where is not possible to use classical hooks or chain slings. The designed hook is consisted of two arms that ensure the stability of the load being carried. The finite element analysis is performed for the control of the stress and deformation state in the whole hook. The fatigue analysis is performed for the check of a lifetime of C-hook

Estimation of Material Properties of Carbon Nanotubes Using Finite Element Method

The paper deals with estimation of material properties of single-walled carbon nanotubes (SWCNTs). The SWCNTs are simulated as frames, where carbon atoms are replaced by nodes and interatomic interactions are replaced by beams. The tension and torsion loading is applied on SWCNTs for determining the elastic modulus, Poisson’s ratio, shear modulus and membrane stiffness of SWCNTs. The simulations for obtaining elongations and torsion angles of SWCNTs are accomplished by the finite element method

SOME DIFFERENTIAL EQUATIONS OF ELASTICITY AND THEIR LIE POINT SYMMETRY GENERATORS

Abstract: The formal models of physical systems are typically written in terms of differential equations. A transformation of the variables in a differential equation forms a symmetry group if it leaves the differential equation invariant. Symmetries of differential equations are very important for understanding of their properties. It can be said that the theory of Lie group symmetries of differential equations is general systematic method for finding solutions of differential equations. Despite of this fact, the Lie group theory is relatively unknown in engineering community. The paper is devoted to some important questions concerning this theory and for several equations resulting from the theory of elasticity their Lie group infinitesimal generators are given