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In the present paper algorithms for constructing a finite element mesh of compound domains and minimizing the ribbon width of the system of resolving equations by the finite element method (FEM) are considered. A technology for constructing a finite element mesh by connecting elementary subdomains, a semi-automatic method for partitioning a two-dimensional multiply connected domain with a curvilinear boundary, and ordering the node numbers of a finite element mesh is described. In this case, the algorithms allow, by ordering the numbering of nodes, to determine such a sequence in which the ribbon width of non-zero coefficients of the system of resolving equations by the FEM will be locally minimal. [ABSTRACT FROM AUTHOR]

This paper presents an approach for a weld connection modeling in the finite element method using the method of Lagrange multipliers. The key issue is to fulfil contact conditions of the weld connection with the possibility to use it for connection of non-conforming meshes. That is why a general node-to-segment (NTS) algorithm which enables to define the connection between nonconforming meshes is used. [ABSTRACT FROM AUTHOR]

In this paper micro-electro-mechanical systems (MEMS) deformable mirror (DM) for its use in adaptive optics in Indus-2 is studied. DMs are used to correct optical aberrations by precisely adjusting the deflection of mirror surface. A piezo based micro-actuator array of 19 keystone shape elements in diameter of 10 mm on silicon of 20 µm thickness is considered for the study. The finite element method (FEM) simulations were carried out using COMSOL Multiphysics 5.4 to estimate the displacement profile. In order to evaluate the applicability of this MEMS based DM in adaptive optics system, piezo response function matrix was determined by applying dc voltage of 1volt to each actuator one by one while keeping the others at zero voltage. The optimum voltage of each actuator to produce a target profile was determined using TLBO algorithm in MATLAB. In this way the obtained voltages are used to generated the low order Zernike mode shapes. [ABSTRACT FROM AUTHOR]

The paper proposes the algorithm for the determination of the coefficients of the Williams series expansion in notched semidisks with different angles of the notch. The algorithm is based on the experimental procedure of the photoelasticity method and the finite element analysis. The large series of experiments for semidiscs was performed. Digital photoelasticity method is used to analyze experimentally the complete Williams series expansion of the stress and displacement fields in the vicinity of the crack tip in isotropic linear elastic plates under Mixed Mode loading. The distribution of the isochromatic fridge patterns is employed for obtaining the stress field near the crack tip by the use of the complete Williams asymptotic expansion for various classes of the experimental specimens (plates with two collinear cracks under tensile loading and under mixed mode loading conditions). The higher order terms of the Williams series expansion are taken into account and the coefficients of the higher order terms are experimentally obtained. The stress field equation of Williams up to fifty terms in each in mode I and mode II has been considered. The comparison of the experimental results and the calculations performed with finite element analysis has shown the importance and significant advantages of photoelastic observations for the multi-parameter description of the stress field in the neighborhood of the crack tip. [ABSTRACT FROM AUTHOR]

The analysis of the interpolation error is particularly important for the error analysis of the finite element methods. In the previous paper, we proved that the finite element solution converges to an exact solution if the maximum circumradius of the triangular elements converges to zero. We call such situation "circumradius condition" and claimed that the circumradius condition is more essential than the well-known maximum angle condition. It is considered that the better finite element solution can be obtained by using the mesh division consists of "good" triangles. However, the generation of such mesh division is time consuming task within the simulation process of the finite element method. On the other hand, the effecient algorithm is known for computing Delaunay triangulation. However, the mesh division produced by Delaunay triangulation sometimes contains collapsed triangles. In this paper, we will introduce "circumradius condition" and show that the effecient error estimate can be obtained by the circumradius condition with Delaunay triangulation. [ABSTRACT FROM AUTHOR]

Improved stability of the node-to-node (NTN) algorithm gained by modification of the algorithm with regard to the explicit method is presented in this paper in order to enable fast and precise analysis of models containing NTN contacts in structural dynamics using Finite Element Method. The key issue is to fulfil contact conditions and prevent solution instability. The instability can be observed if the time step exceeds the critical time step, which is directly derived from the element stiffness and tends towards zero as connected nodes get closer to each other [1]. This is the main problem of NTN contacts in the explicit method. [ABSTRACT FROM AUTHOR]

The paper deals with the development of the technique for J-integral computation using the vector fields obtained by digital image correlation method. The proposed computing algorithm includes several steps following each other: (i) construction of displacement vector field; (ii) calculation of deformations and stresses; (iii) calculation of the J-integral value. A comparative study of the results obtained by the proposed technique and by finite element simulation was carried out. The errors of the data modeled in the ANSYS from the computed J-integral values were estimated at various tensile loads. [ABSTRACT FROM AUTHOR]

The paper presents results of applying various approaches to simulation of contact surfaces fracture under high velocity interaction of solid bodies. Three basic methods have been distinguished having the difference in the algorithms of mass distribution after elements fracture at contact boundaries. Authors own finite element computer software program EFES has been used for the calculations. The calculation was carried out in a complete three-dimensional formulation. The obtained results using all three algorithms have been compared to the experimental results. [ABSTRACT FROM AUTHOR]

In order to describe the meso-damage of the refractories more accurately, and to study of the relationship between the mesostructured of the refractories and the macro-mechanics, this paper takes the magnesia-carbon refractories as the research object and uses the molecular dynamics method to instead the traditional sequential algorithm to establish the meso-particles filling model including small and large particles. Finally, the finite element software-ABAQUS is used to conducts numerical simulation on the meso-damage evolution process of refractory materials. From the results, the process of initiation and propagation of microscopic interface cracks can be observed intuitively, and the macroscopic stress-strain curve of the refractory material is obtained. The results show that the combination of molecular dynamics modeling and the use of Python in the interface to insert the cohesive element numerical simulation, obtaining of more accurate interface parameters through parameter inversion, can be more accurate to observe the interface of the meso-damage evolution process and effective to consider the effect of the mesostructured of the refractory material on its macroscopic mechanical properties. [ABSTRACT FROM AUTHOR]

The goal of this paper is to solve the post buckling phenomena of a large deformed elastic beam by a canonical dual mixed finite element method (CD-FEM). The total potential energy of this beam is a nonconvex functional which can be used to model both pre-and post-buckling problems. Different types of dual stress interpolations are used in order to verify the triality theory. Applications are illustrated with different boundary conditions and external loads by using semi-definite programming (SDP) algorithm. The results show that the global minimum of the total potential energy is stable buckled configuration, the local maximum solution leads to the unbuckled state, and both of these two solutions are numerically stable. While the local minimum is unstable buckled configuration and very sensitive to both stress interpolations and the external loads. [ABSTRACT FROM AUTHOR]