In this paper, based on the classical Fourth-Order Runge-Kutta method, the modified FourthOrder Runge-Kutta method is presented for solving nonlinear vibration of axially travelling string system, that is to solve time varying and nonlinear differential equations. The classical Fourth-Order Runge-Kutta method can only be used to solve first-order linear differential equations. Its main idea is ...

This paper presents an improved approach where the wavelet functions are developed for particularly two-dimensional (2D) trusses. In the proposed scheme, a clear-cut formulation in a fluent manner has been derived to numerically solve the second-ordered differential equation of motion governing 2D trusses using two different types of basis functions including, complicated Chebyshev and simple H...

The morphology of telephone-cord buckles of elastic thin films can be used to evaluate the initial residual stress and interface toughness of the filmsubstrate system. The maximum out-of-plane displacement δ, the wavelength λ and amplitude A of the wave buckles can be measured in physical experiments. Through δ, λ, and A, the buckle morphology is obtained by an annular sector model established ...

A general approach to the dimensional reduction of non-linear nite element models of solid dynamics is presented. For the Newmark implicit time-discretization, the computationally most expensive phase is the repeated solution of the system of linear equations for displacement increments. To deal with this, it is shown how the problem can be formulated in an approximation (Ritz) basis of much sm...

An advanced physics-based simulation of firearms injury to the human cranium is presented, modeling by finite elements the collision of a firearm projectile into a human parietal bone. The space-discretized equations of motion are explicitly integrated in time with Newmark’s time-stepping algorithm. The impact of the projectile on the skull, as well as the collisions between flying fragments, a...

Strong earthquake excitation usually induces large shear strains to earth structures resulting to the generation of low shear-strength surfaces, and subsequently, to sliding along these surfaces. The generation of permanent deformations is a phenomenon commonly examined through the well-known procedure of sliding block proposed by Newmark. Nevertheless, many types of earth structures include pr...

This paper investigates the application of Artificial Bee Colony (ABC) method for the optimization of Tuned Mass Dampers (TMDs) employed for high-rise structures including Soil Structure Interaction (SSI). The model is a 40-story building, and Newmark method is utilized for the structure response to Bam earthquake data. The objective is to decrease both maximum displacement and accelerati...

This paper is concerned with the convergence analysis of PH heterogeneous asynchronous time integrators algorithm, proposed by Prakash and Hjelmstad [ Int. J. Numer. Methods Eng. 61 (2004) 2183–2204], devoted to transient dynamic problems for structural analysis. According method, discretization performed using well-known Newmark schemes, where step ratio, i.e. , ratio macro micro step, two sub...

This paper investigates a time-stepping procedure of the Newmark type for dynamic analyses viscoelastic structures characterized by generalized Maxwell model. We depart from scheme developed three-parameter model Hatada et al. [1], which we extend to generic chain and demonstrate that resulting algorithm can be derived suitably discretized Hamilton variational principle. structure manifests its...