Functional continuous Runge–Kutta–Nyström methods

Numerical methods for solving retarded functional differential equations of the second order with right-hand side independent of the function derivative are considered. The approach used by E. Nyström for second-order ordinary differential equations with the mentioned property is applied for construction of effective functional continuous methods. Order conditions are formulated, and example methods are constructed. They have fewer stages than Runge–Kutta type methods of the same order. Application of the constructed methods to test problems confirms their declared orders of convergence

Piezoelectric fiber mats containing polar rod-shaped pigment particles

We demonstrate converse piezoelectric behavior of electrospun polylactic acid (PLA) fiber mats containing anisometric pigment nanoparticles (Novoperm Carmine HF3C). The effective piezoelectric constant of the fiber mats was estimated to be 2 nm V-1. These findings suggest polarity of the pigment particles obtained by a milling process. Transient electric current measurements were conducted to test the residual polarization of the particles. Piezoelectric fiber mats may be utilized to make colorful electro-active fiber mats and wearable smart clothing

Solving Boundary Value Problem for a Nonlinear Stationary Controllable System with Synthesizing Control

An algorithm for constructing a control function that transfers a wide class of stationary nonlinear systems of ordinary differential equations from an initial state to a final state under certain control restrictions is proposed. The algorithm is designed to be convenient for numerical implementation. A constructive criterion of the desired transfer possibility is presented. The problem of an interorbital flight is considered as a test example and it is simulated numerically with the presented method.Comment: 9 pages, 2 figure

Estimating degradation of strength of neat PEEK and PEEK-CF laminates under cyclic loading by mechanical hysteresis loops

A method for assessing the degradation of mechanical properties of neat polyetheretherketone and its laminated composite reinforced with unidirectional carbon fibers is proposed. It is based on the calculation of the maximum and minimum strains in a cycle, as well as both dynamic and secant moduli estimated from mechanical hysteresis loops. These parameters reflect the material damage degree, enabling to predict its current mechanical state