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Abstract: The Immersed Boundary (IB) method is a widely-used numerical methodology for the simulation of fluid–structure interaction problems. The IB method utilizes an Eulerian discretization for the fluid equations of motion while maintaining a Lagrangian representation of structural objects. Operators are defined for transmitting information (forces and velocities) between these two representations. Most IB simulations represent their structures with piecewise linear approximations and utilize Hookean spring models to approximate structural forces. Our specific motivation is the modeling of platelets in hemodynamic flows. In this paper, we study two alternative representations – radial basis functions (RBFs) and Fourier-based (trigonometric polynomials and spherical harmonics) representations – for the modeling of platelets in two and three dimensions within the IB framework, and compare our results with the traditional piecewise linear approximation methodology. For different representative shapes, we examine the geometric modeling errors (position and normal vectors), force computation errors, and computational cost and provide an engineering trade-off strategy for when and why one might select to employ these different representations. [Copyright &y& Elsevier]

Abstract: In the present paper the finite element method for the solution of the eigenvalue problems for piezoelectric bodies with voids is considered. The porosity change properties are taken into account according to Cowin–Nunziato model. The vector–matrix formulations of the modal piezoelectric problems for media with voids are given. The finite element approximations of the continual equations are carried out and the finite dimensional eigenvalue problems are obtained in the expanded and in the various reduced forms. Algorithmic features of the boundary conditions account for electrode surfaces and the surfaces contacting with rigid stamps are discussed. The finite element eigenvalue problems for practically important electric resonance and antiresonance frequencies are obtained. As a numerical example the focusing spherical ultrasonic piezoelectric emitter fulfilled from porous piezoceramics is considered. With the use of Cowin–Nunziato model the effective moduli of the porous piezoceramic material are defined precisely. The results, which we obtain, show a good optimal agreement with the experimental data. The resonant frequency behavior modelling for free and loaded on acoustic media piezoelectric transducer is realized. [Copyright &y& Elsevier]

Abstract: In the present paper, static and dynamical problems for linearly elastic shells in curvilinear coordinates are considered. Hierarchies of two-dimensional models for corresponding boundary and initial boundary value problems are constructed within the variational settings. The existence and uniqueness of solutions of the reduced problems are investigated in suitable spaces. Under the conditions of solvability of the original static or dynamical problem, convergence of the sequence of vector functions of three variables restored from the solutions of the constructed two-dimensional problems to the solution of the three-dimensional problem is proved and approximation error is estimated. [Copyright &y& Elsevier]