A CORDIC- based shift-add algorithm for generating B-spline curves is presented in this paper. This algorithm can be realized by hardware without multiplier, or coded with assembly language and run in the basic computing system which exists in many application systems. Convergence of the algorithm was proved. Errors were estimated and well controlled in the algorithm. A numerical experiment was carried out to validate algorithm. This algorithm can be used for adding complex curve plotting functions in embedded systems.


Keywords: B-spline, CORDIC, shift-add algorithm, basic computing system.

The main interest of pharmacokinetics is the study of the fate of drugs in the living organism. This work proposes the system of the conservation laws that describes time-dependent concentrations of a drug, after a single intravenous administration. Compared with others, the proposed model considers both free and protein-bound drug concentrations at the same time. Plasma protein binding captured in the model enters the nonlinearity arising from the Guldberg-Waage law. According to our best knowledge, the analytical solution for our system does not exist. Our model allows the calculation of the free and bound-drug protein concentrations at any time point and at any dose after single intravenous bolus dose administration. In order to compare the empirical with simulated data, a numerical approach has been proposed. On the basis of published experimental data the model validation has been carried out. The goodness of fit was satisfactory (R² = 0.99) and the experimental and simulated AUC (area under the curve) values, as the measure of the bioavailability of drug, were similar (150 M/hxh^-¹). The preliminary assessment of the model credibility was positive and encouraged further studies.


Keywords: evolution equations, non-linear model, drug protein binding.

The paper contains some estimates of an approximation to the solution of the problem of acoustic waves's scattering by an elastic obstacle in two dimensions. The problem is approximated by the isogeometric adaptive method based on the known NURBS functions. The estimates show how the error of an approximation depends on the size of intervals and the degree of functions.


Keywords: NURBS, adaptive methods, error estimates, acoustic scattering.

The effective mechanical properties and the stress-strain relations of the eight types of the graphene allotropes are presented in this paper. Series of the tensile and shear tests are performed using the non-equilibrium molecular dynamics (NEMD) and the adaptive intermolecular reactive bond order (AIREBO) potential. The methodology of the investigation as well as obtained results are explained and discussed in detail. Where possible, the achieved results are compared with the data available in the scientific literature in order to validate our molecular dynamics models and simulations. In other cases, i.e., where only information about structural or electronic properties is available, presented results can complement the knowledge about these particular planar carbon networks.


Keywords: graphene, nanomechanics, molecular dynamics, mechanical properties.

The paper deals with the identification in multiscale analysis of structures under thermal and mechanical loads. A two-scale model of porous materials is examined. Direct thermoelastic analyses with representative volume element (RVE) and finite element method (FEM) are taken into account. Identification of material constants of the microstructure and identification of the shape of the voids in the microstructure are considered. Identification functional is formulated on the basis of information obtained from measurements in mechanical and thermal fields. Evolutionary algorithm is used for the identification as the optimization technique. Numerical examples of identification for porous aluminum models are enclosed.


Keywords: multiscale modeling, numerical homogenization, thermoelasticity, evolutionary algorithms, identification, coupled problems, finite element method.

Inverse form finding aims to determine the optimum blank design of a workpiece whereby the desired spatial configuration that is obtained after a forming process, the boundary conditions and the applied loads are known. Inputting the optimal material configuration, a subsequent FEM computation then has to result exactly in the nodal coordinates of the desired deformed workpiece. Germain et al. [1] recently presented a new form finding strategy for isotropic elastoplasticity. Switching between the direct and the inverse mechanical formulation, while fixing the internal plastic variables in the inverse step, uniquely detects the undeformed configuration iteratively. In this contribution, the developed recursive algorithm is extended to anisotropic plasticity. In particular the orthotropic Hill yield function is considered. A load and a displacement-controlled example demonstrate that this new strategy requires only a few iterations to determine the optimal initial design whereby an almost linear convergence rate is obtained.


Keywords: inverse FEM, inverse form finding, orthotropic Hill's yield criterion, logarithmic strain space, optimum blank design.