Soft-impact dynamics of deformable bodies

Systems constituted by impacting beams and rods of non-negligible mass are often encountered in many applications of engineering practice. The impact between two rigid bodies is an intrinsically indeterminate problem due to the arbitrariness of the velocities after the instantaneous impact and implicates an infinite value of the contact force. The arbitrariness of after-impact velocities is solved by releasing the impenetrability condition as an internal constraint of the bodies and by allowing for elastic deformations at contact during an impact of finite duration. In this paper, the latter goal is achieved by interposing a concentrate spring between a beam and a rod at their contact point, simulating the deformability of impacting bodies at the interaction zones. A reliable and convenient method for determining impact forces is also presented. An example of engineering interest is carried out: a flexible beam that impacts on an axially deformable strut. The solution of motion under a harmonic excitation of the beam built-in base is found in terms of transverse and axial displacements of the beam and rod, respectively, by superimposition of a finite number of modal contributions. Numerical investigations are performed in order to examine the influence of the rigidity of the contact spring and of the ratio between the first natural frequencies of the beam and the rod, respectively, on the system response, namely impact velocity, maximum displacement, spring stretching and contact force. Impact velocity diagrams, nonlinear resonance curves and phase portraits are presented to determine regions of periodic motion with impacts and the appearance of chaotic solutions, and parameter ranges where the functionality of the non-structural element is at risk.     

Study of the dynamic contact interaction of deformable bodies

A new algorithm for solving dynamic contact problems involving deformable bodies is proposed. The algorithm is based on formulation of the boundary conditions for the contact interaction with allowance for Coulomb friction in the form of quasivariational inequalities. The algorithm is numerically stable and satisfies geometric constraints in the a priori unknown contact region and conditions specifying that the normal pressure be nonnegative and that the vectors describing tangential velocity and shear stress during slip be oppositely directed. Results are presented from calculations performed for a contact problem for an elastoplastic body in a two-dimensional formulation. Computer Center, Siberian Division, Russian Academy of Sciences, Krasnoyarsk 660036. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 4, pp. 167–173, July–August, 1998.     

Three-dimensional problems of mechanics of deformable bodies of noncanonical shape

The paper is based on the author's report at the General Jubilee Meeting of the Mechanics Division on the occasion of the 80th anniversary of the National Academy of Sciences of Ukraine. Results obtained in the subject area “mechanics of deformable bodies of noncanonical shape” are discussed. This subject area was formed at the S. P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine on the basis of variants of the analytical method of boundary-shape perturbation proposed and developed at the Institute. The objects of investigation and the classification of three-dimensional boundary-value problems for noncanonical areas are analyzed. Tests of the accuracy of approximate solutions obtained using the developed analytical methods are indicated. Presented at General Meeting of Mechanics Division of National Academy of Sciences of Ukraine (Kiev, November 30, 1998). S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 10, pp. 3–20, October, 1999.     

Some computational aspects for analysis of low- and high-velocity impact of deformable bodies

In this paper, we present some numerical algorithms devoted to analysis of low- and high-velocity impact of deformable bodies. For modeling of contact phenomena involved in impact problems, an implicit method is used rather than the most popular penalty explicit method. For the appropriate time integration of the discretized equation of motion, a first order algorithm is suggested rather than the most common second order algorithms such as Newmark, Wilson, etc. Numerical results are presented for dynamic analysis such as low-velocity impact of an elastic plate on a rigid surface with rebounding and high-velocity impact of an elastic-plastic copper bar on a rigid wall.     

Dynamic interaction of fixed dual spheres for several configurations and inflow conditions

The changes in force characteristics as well as the shedding patterns for various dual sphere configurations are studied. The Reynolds numbers considered are 300, 600 and two different inflow conditions are used: steady and pulsating. The sphere formations are defined by the separation distance D₀ between the spheres and the angle between the line connecting the centres of the spheres and the main flow direction, γ. The position of one of the spheres is varied in the range 0°–90° using a 15° increment. Two separation distances are studied; 1.5D and 3D. The method used for the simulations is the Volume of Solid (VOS) approach, a method based on Volume of Fluid (VOF). A major conclusion from this work is that the sphere interaction alters the wake dynamics by obstructing the vortex shedding (generating a steady wake or a wake with lower Strouhal number) and by changing the direction of the lift force so that it in most cases is directed in the plane containing the sphere centres. The results also show that changing the inflow condition gives the same relative change in drag and lift as for a single sphere. The drag is substantially reduced by placing the sphere downstream in a tandem arrangement and slightly increased in a side-by-side arrangement. However, the effect is decreased by increasing separation distance and increasing Reynolds number.