Showing papers by "Vladimir Sladek published in 2022"

The Importance of Charge Transfer and Solvent Screening in the Interactions of Backbones and Functional Groups in Amino Acid Residues and Nucleotides

Abstract: Quantum mechanical (QM) calculations at the level of density-functional tight-binding are applied to a protein–DNA complex (PDB: 2o8b) consisting of 3763 atoms, averaging 100 snapshots from molecular dynamics simulations. A detailed comparison of QM and force field (Amber) results is presented. It is shown that, when solvent screening is taken into account, the contributions of the backbones are small, and the binding of nucleotides in the double helix is governed by the base–base interactions. On the other hand, the backbones can make a substantial contribution to the binding of amino acid residues to nucleotides and other residues. The effect of charge transfer on the interactions is also analyzed, revealing that the actual charge of nucleotides and amino acid residues can differ by as much as 6 and 8% from the formal integer charge, respectively. The effect of interactions on topological models (protein -residue networks) is elucidated.

Love waves propagation in layered waveguide structures including flexomagneticity/flexoelectricity and micro-inertia effects

Abstract: A gradient-type theory with flexomagnetic/flexoelectric and micro-inertia effects is used to study Love wave propagation in the layered magneto-electro-elastic structures. Two waveguide structures are considered: flexo-piezoelectric layer deposited on the piezomagnetic half-space and flexo-piezomagnetic layer resting on the piezoelectric half-space. The dispersion equations are numerically investigated for the magneto-electrically open and short circuit conditions. It is concluded that the profile of dispersion curves depends on the material composition of the waveguide structure, the guiding layer thickness, and the relative values of flexomagnetic/flexoelectric coefficients and the micro-inertia length-scale parameter. The obtained results are helpful for mathematical modeling of new small-sized acoustic devices.

Meshless finite block method with infinite elements for axisymmetric cracked solid made of functionally graded materials

Abstract: Axisymmetric cracked solid structures in functionally graded materials (FGMs) under static and dynamic loading are analysed by using the Finite Block Method (FBM). Based on the axisymmetric elasticity theory, the equilibrium equations inside the rotating section of FGMs in the cylinder coordinate system are formulated in strong form. The shape functions in the FBM are constructed by Lagrange polynomial interpolation with mapping techniques for the irregular finite or semi-infinite physical domains. A special approximation technique is proposed to avoid singularities in the traction boundary conditions on the axis of symmetry. The stress intensity factor is obtained by the crack opening displacement. The time-dependent problems are addressed using the Laplace transform and Durbin's inverse approach. Several numerical examples are investigated in order to illustrate the accuracy and convergence of the proposed method, and the numerical solutions are compared with analytical solutions, the finite element method and other methods.

A Strong Form Meshless Method for the Solution of FGM Plates

Abstract: Laminated composite structures suffer from failure because of concentrations of gradient fields on interfaces due to discontinuity of material properties. The rapid development of material science enables designers to replace classical laminated plate elements in aerospace structures with more advanced ones made of functionally graded materials (FGM), which are microscopic composite materials with continuous variation of material coefficients according to the contents of their micro-constituents. Utilization of FGM eliminates the inconvenience of laminated structures but gives rise to substantial changes in structural design This paper deals with the presentation of a strong formulation meshless method for the solution of FGM composite plates. Recall that the fourth-order derivatives of deflections are involved in the governing equations for plate structures. However, the high-order derivatives of field variables in partial differential equations (PDE) lead to increasing inaccuracy of approximations. For that reason, the decomposition of the high-order governing equations into the second-order PDE is proposed. For the spatial approximation of field variables, the meshless moving least square (MLS) approximation technique is employed. The reliability (numerical stability, convergence, and accuracy) as well as computational efficiency of the developed method is illustrated by several numerical investigations of the response of FGM plates with the transversal gradation of material coefficients under stationary and/or transient mechanical and thermal loadings.

Influence of flexoelectricity on an interface crack between two dissimilar dielectric materials

Abstract: In the present paper, the interface crack between two dissimilar dielectric materials under a mechanical load is investigated with including flexoelectricity effects. Flexoelectricity is a size dependent electro-mechanical coupling phenomenon, where the electric polarization is induced by a strain gradient in dielectrics. The strain gradients may potentially break the inversion symmetry in centrosymmetric crystals and polarization is observed even in all dielectric materials. The polarization is proportional to the strain gradients in the direct flexoelectricity. Layered composite structures are frequently utilized in microelectronics. Due to a poor adhesion of protection layer and basic material, the interface crack can be created there and for the prediction of failure of these structures it becomes essential to investigate distribution of the interfacial stress and strain fields. Governing equations in the gradient theory contain higher-order derivatives than in the standard continuum mechanics. Therefore, a reliable computational tool is required to solve these boundary-value problems. The mixed finite element method (FEM) is developed, where the standard C° continuous finite elements are utilized for independent approximations of displacements and strains. The constraints between the strain gradients and displacements are satisfied by collocation at Gaussian integration points inside elements. In numerical examples, a parametric study is performed with respect to flexoelectric and elastic coefficients for both material regions. The influence of these parameters on the crack opening displacement is discussed.

Semi-Infinite Structure Analysis with Bimodular Materials with Infinite Element

Abstract: The modulus of elasticity of some materials changes under tensile and compressive states is simulated by constructing a typical material nonlinearity in a numerical analysis in this paper. The meshless Finite Block Method (FBM) has been developed to deal with 3D semi-infinite structures in the bimodular materials in this paper. The Lagrange polynomial interpolation is utilized to construct the meshless shape function with the mapping technique to transform the irregular finite domain or semi-infinite physical solids into a normalized domain. A shear modulus strategy is developed to present the nonlinear characteristics of bimodular material. In order to verify the efficiency and accuracy of FBM, the numerical results are compared with both analytical and numerical solutions provided by Finite Element Method (FEM) in four examples.

Transient Analysis of Micro/Nano Plates by Moving Finite Element Method

Abstract: The paper deals with transient analysis of homogeneous as well as FGM (functionally graded material) thin micro/nano plates subjected to transversal dynamic loading. within the highergrade continuum theory of elasticity. The microscopic structure of material is reflected in this higher-grade continuum theory via one material coefficient called the micro-length scale parameter. Furthermore the material can be composed of two micro-constituents what is included in the employed continuum model by functional gradation of the Young’s modulus through the plate thickness with assuming power-law dependence of volume fractions of micro-constituents on the transversal coordinate. The high order derivatives of field variables are eliminated by decomposing the original governing partial differential equations (PDE) into the system of PDEs with lower order derivatives. For the numerical implementation, the weak formulation is proposed with novel Moving Finite Element approximation method of spatial variations of field variables. The semi-discretized equations of motion yield a system of ordinary differential equations which can be solved by standard time stepping techniques. Several numerical simulations are devoted to study the influence of micro-length scale parameter as well as the parameters of gradation of Young’s modulus on coupled bending and in-plane deformation response modes.