Impact loading of plates and shells by free-flying projectiles: A review

Simulation of welding has advanced from the analysis of laboratory setups to real engineering applications during the last three decades. This development is outlined and the directions for future research are summarized in this review, which consists of three parts. This part shows that the increased complexity of the models gives a better description of the engineering applications. The important development of material modeling and computational efficiency are outlined in Parts 2 and 3, respectively.

Finite element modeling and simulation of welding part 1: increased complexity

A formulation is presented for the nonlinear dynamics of initially curved and twisted anisotropic beams. When the applied loads at the ends of, and distributed along, the beam are independent of the deformation, neither displacement nor rotation variables appear: an intrinsic formulation. Like well-known special cases of these equations governing nonlinear dynamics of rigid bodies and nonlinear statics of beams, the complete set of intrinsic equations has a maximum degree of nonlinearity equal to two. Advantages of such a formulation are demonstrated with a simple example. When the initial curvature and twist are constant along the beam, two space-time conservation laws are shown to exist, one being a work-energy relation and the other a generalized impulse-momentum relation. These laws can be used, for example, as benchmarks to check the accuracy of any proposed solution, including time-marching and finite element schemes. The structure of the intrinsic equations suggests parallel approaches to spatial and temporal discretization. A particularly simple spatial discretization scheme is presented for the special case of the nonlinear static behavior of end-loaded beams that, by virtue of the Kirchhoff analogy, leads to a time-marching scheme for the dynamics of a pivoted rigid body in a gravity field. This time-marching scheme conserves both the angular momentum about a vertical line passing through the pivot and total mechanical energy, whereas the analogous spatial discretization scheme for the nonlinear static behavior of end-loaded beams satisfies analogous integrals of deformation along the beam span. Remarkably, a straightforward generalization of these discretization schemes is shown to satisfy both space-time conservation laws for the nonlinear dynamics of beams when the applied loads are constant within a space-time element.

Geometrically Exact, Intrinsic Theory for Dynamics of Curved and Twisted Anisotropic Beams

Nonlinear vibrations of suspended cables—Part I: Modeling and analysis

Review of composite rotor blade modeling

A large deformation, small-strain theory is presented for heterogeneous, transverse isotropic, elastic rods with pre-twist. The theory is applicable to practical problems related to the dynamics of cable systems, helicopter blades, space antennae, and similar structures. Two elementary examples are included: reduction of the general theory to particular differential equations governing the planar, steady-state towing of cables, and the steadystate motion of helicopter rotor blades.

A nonlinear dynamical theory for heterogeneous, anisotropic, elasticrods

The dynamic behavior of an elastic catenary cable due to a moving mass alongits length is investigated. The equations of motions are derived using theHamilton's principle for general supports that include the horizontal andinclined cables with small and large sags and for variable velocity of themoving mass. Those equations of motions are in general nonlinear partialdifferential equations due to the initial curvature of the cable. Theequations are also complex due to the presence of three different types ofaccelerations of the moving mass. Those are the normal, Coriolis andcentrifugal accelerations. Therefore, we used the Galerkin procedure withsine function (Fourier representation) and anti-derivative functions of thecompactly supported wavelets as trial basis and used direct integrationmethods to integrate the discretized equations of motions. Newton–Raphsonmethod is used for iterations. Several examples are studied and the resultsas obtained by Fourier and wavelet representations are compared. Because ofthe localization feature, wavelets are proven to minimize the spuriousoscillations specially those appearing in the cable tension.

Dynamics of an Elastic Cable Carrying a Moving Mass Particle

Interfacial waves in incompressible monoclinic materials with an interlayer

The reflection of plane elastic waves from a free surface of monoclinic incompressible materials is examined under plane strain conditions in a plane of material symmetry. It is found that this problem can be equivalently treated by elastic wave reflection in orthotropic incompressible materials if the material constants of the monoclinic material are properly related to those of the orthotropic material. Thus the range of existence of the two (one homogeneous and the other homogeneous or inhomogeneous) reflected waves in a monoclinic material, including points corresponding to zero amplitude reflected waves, can be obtained from that given in a previous paper [Nair and Sotiropoulos, J. Acoust. Soc. Am. 102, 102–109 (1997)] where an orthotropic material was treated.

S. Nair

Papers

A nonlinear dynamical theory for heterogeneous, anisotropic, elasticrods

Dynamics of an Elastic Cable Carrying a Moving Mass Particle

Interfacial waves in incompressible monoclinic materials with an interlayer

Elastic waves in orthotropic incompressible materials and reflection from an interface

Wavelet-Galerkin method for the free vibrations of an elastic cable carrying an attached mass