Analytical solutions of impact problems of rod structures with springs

a b s t r a c tCertain types of structures and materials, such as engineered multi-scale systems and comminuted zones in failed ceramics, may be modeled using continuum theories incorporating additional kinematic degrees of freedom beyond the scope of classical continuum theories. If such material systems are to be subjected to high strain rate loads, such as those resulting from ballistic impact or blast, it will be necessary to develop models capable of describing transient stress wave propagation through these media. Such a model is formulated, solved, and applied to the impact between two bodies and to a two-layer bar or strip subjected to an instantaneously applied stress. Results from these examples suggest that the model parameters, and therefore constitutive properties and geometries, may be tuned to reduce and control the transmission of stress through these bodies.Published by Elsevier Ltd.

show abstract

“…Therefore, the initial conditions must specify both the initial velocities as in YuFeng and DeChao (1998) and Goldsmith (1999):…”

Section: Boundary and Initial Conditions For The Impact Problemmentioning

confidence: 99%

Transient stress wave propagation in one-dimensional micropolar bodies

Randow

Gazonas

2009

International Journal of Solids and Structures

View full text Add to dashboard Cite

show abstract

“…The solution of the nonlinear ordinary differential equation (11) had been earlier solved by Lagrange (a kinetic analogy of columns [1]). Integrating Eq.…”

Section: Postbuckling Solutionmentioning

confidence: 99%

“…Yin and Wang [10] studied the subcritical behavior of elastic clamped-free rods with constant original curvature under force load acting at the free end, where, in particular, the load-displacement characteristics (spring behavior) were examined. YuFeng and DeChao [11] developed the analytical solutions of rigid (without contact deformation) impact problems for two typical rod structures with elastic supports and thoroughly analyzed the boundary conditions effect on wave propagation and impact response. Da Silva et al [12] presented analytical solutions for the evaluation of steel connections, which could reproduce the full nonlinear system behavior using an elastic postbuckling model with two equivalent elastic springs.…”

mentioning

confidence: 99%

Thermal Postbuckling of Slender Elastic Rods With Hinged Ends Constrained by a Linear Spring

Vaz¹,

Solano²

2004

Journal of Thermal Stresses

View full text Add to dashboard Cite

“…Here we refer, e.g. to Feng and Chao [6] applying eigenfunctions with trigonometric functions in time. Usually a rather arbitrary number of eigenfunctions is used in the solution series, resulting in e.g.…”

mentioning

confidence: 99%

“…Usually a rather arbitrary number of eigenfunctions is used in the solution series, resulting in e.g. 1000 terms in [6]. However, often the discussion of any convergence study with respect to a finite summation is missing.…”

mentioning

confidence: 99%

Impact of an elastic rod on a deformable barrier: analytical and numerical investigations on models of a valve and a rod-shaped stamping tool

et al. 2009

View full text Add to dashboard Cite

The longitudinal motion of an elastic rod is studied for the case that the rod is suddenly elastically fixed at one end and is hit by a mass at its other end. This configuration represents real settings e.g. as a valve impacts an elastic valve-seat or as a stamping device used in forging is hit by a large mass. The solution of the problem is formulated in the Laplace transformation space. The inverse transformation into the time domain is performed by engaging the so-called Laguerre polynomial technique. This method allows to calculate exact solutions for finite times from a finite number of series elements. Rigorous mathematical proofs not established up to now are given with respect to the convergence of the series encountered and the validity of exchanging the order of inversion of the Laplace transformation and summation of the established series. For comparison also a numerical solution of the problem is presented. An analysis of the energy transfer between rod, impacting mass and elastic barrier elucidates the marked influence of the deformability of the elastic barrier on the stress state in the rod.

show abstract

Analytical solutions of impact problems of rod structures with springs

Cited by 16 publications

References 0 publications

Transient stress wave propagation in one-dimensional micropolar bodies

Transient stress wave propagation in one-dimensional micropolar bodies

Thermal Postbuckling of Slender Elastic Rods With Hinged Ends Constrained by a Linear Spring

Impact of an elastic rod on a deformable barrier: analytical and numerical investigations on models of a valve and a rod-shaped stamping tool

Contact Info

Product

Resources

About