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Razdolsky A.G.,Independent Research Scientist
International Journal of Computational Methods in Engineering Science and Mechanics

It is known that elastic large deflections of thin plates are governed by von Karman nonlinear equations. The analytical solution of these equations in the general case is unfeasible. Samuel Levy, in 1942, showed that large deflections of the rectangular plate can be expressed as a double series of sine-shaped harmonics (deflection harmonics). However, this method gave no way of creating the computer algorithm of solving the problem. The stress function expression taken in the Levy's method must be revised to find the approach that takes into account of all possible products of deflection coefficients. The algorithm of solving the problem for the rectangular plate with an arbitrary aspect ratio under the action of the lateral distributed load is reported in this paper. The approximation of the plate deflection is taken in the form of double series proposed by Samuel Levy. However, the expression for the stress function is presented in the form that incorporates products of deflection coefficients in the explicit form in distinction to the Levy's expression. The number of harmonics in the deflection expression may be arbitrary. The algorithm provides composing the system of governing cubic equations, which includes the deflection coefficients in the explicit form. Solving the equation system is based on using the principle of minimum potential energy. A method of the gradient descent is applied to find the equilibrium state of the plate as the minimum point of the potential energy. A computer program is developed on the basis of the present algorithm. Numerical examples carried out for the plate model with 16 deflection harmonics illustrate the potentialities of the program. The results of solving the examples are presented in the graphical form for the plates with a different aspect ratio and may be used under designing thin-walled elements of airplane and ship structures. © 2015 Taylor and Francis Group, LLC. Source

Razdolsky A.G.,Independent Research Scientist
Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME

Motion of the hoisting rope carrying an intermediate concentrated load is described by the one-dimensional wave equation in the region consisting of two sections separated by a moving boundary condition. The system is moved by the driving force acting at the upper cross section of the rope. Position of the intermediate load and consequently the lengths of the rope sections vary in the time depending on the magnitude of driving force. Solution of the wave equation is represented as a sum of integrals with variable limits of integration. The problem is reduced to solving the sequence of ordinary differential equations which describe a motion of the load in the fixed coordinate system and the paths of the rope ends in the moving coordinate system connected with the load. The argument of functions involved in the right-hand side of these equations lag behind the argument of the derivatives in the left-hand side of equations by a short time interval. A description of the unknown functions in a parametric form makes possible to eliminate retarded arguments from the equations. The problem is solved by using a technique of the sequential continuation of solution for time intervals corresponding to propagation of the deformation wave in the opposite directions. A computer program has been developed for solving the problem. Results of the numerical solution are presented in the case that the driving force is a piecewise linear function of time and is discontinuous at the peak point. © 2014 by ASME. Source

Razdolsky A.G.,Independent Research Scientist
Journal of Engineering Mechanics

Solving the buckling problem for a battened column as a statically indeterminate structure yields a Euler critical load that is significantly higher than the buckling load being obtained on the basis of Engesser's assumption. The stability problem is reduced to numerically solving a two-point boundary value problem for a system of recurrence relations between deformation parameters of adjacent joint cross sections of the column. The expression of deformation parameters for each further joint cross section of the column as a linear function of deformation parameters for the preceding joint cross section is possible using the initial-value method. For columns with any degree of static indeterminacy, the critical force is determined as the smallest eigenvalue of the fourth-order system of homogeneous linear algebraic equations. A computer realization of the present method requires implementing reorthogonalization of the vectors of particular solutions for the system of recurrence relations. Plots of the buckling load for columns with any number of panels can be constructed as a function of the batten rigidity parameter. Applying these plots can be useful in selecting a cross section of the columns being designed. © 2014 American Society of Civil Engineers. Source

Subpaiboonkit S.,Chiang Mai University | Thammarongtham C.,Biochemical Engineering and Pilot Plant Research and Development Unit | Cutler R.W.,Independent Research Scientist | Chaijaruwanich J.,Chiang Mai University
International Journal of Data Mining and Bioinformatics

Non-coding RNAs (ncRNAs) have important biological functions in living cells dependent on their conserved secondary structures. Here, we focus on computational RNA secondary structure prediction by exploring primary sequences and complementary base pair interactions using the Conditional Random Fields (CRFs) model, which treats RNA prediction as a sequence labelling problem. Proposing suitable feature extraction from known RNA secondary structures, we developed a feature extraction based on natural RNA's loop and stem characteristics. Our CRFs models can predict the secondary structures of the test RNAs with optimal F-score prediction between 56.61 and 98.20% for different RNA families. Copyright © 2013 Inderscience Enterprises Ltd. Source

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