Impact response of a thin shallow doubly curved linear viscoelastic shell rectangular in plan

In this paper, we consider the problem on a transverse impact of a viscoelastic sphere upon a viscoelastic shallow doubly curved shell with rectangular platform, the viscoelastic features of which are defined via the fractional derivative standard linear solid models; in so doing, only Young’s time-dependent operators are preassigned, while the bulk moduli are considered to be constant values, since the bulk relaxation for the majority of materials is far less than the shear relaxation. Shallow panel’s displacement subjected to the concentrated contact force is found by the method of expansion in terms of eigen functions, and the sphere’s displacement under the action of the contact force, which is the sum of the shell’s displacement at the place of contact and local bearing of impactor and target’s materials, is defined from the equation of motion of the material point with the mass equal to sphere’s mass. Within the contact domain, the contact force is defined by the modified Hertzian contact law with the time-dependent rigidity function. For decoding the viscoelastic operators involving the problem under consideration, the algebra of Rabotnov’s fractional operators is employed. A nonlinear integro-differential equation is obtained either in terms of the contact force or in the local bearing of the target and impactor materials. Using the duration of contact as a small parameter, approximate analytical solutions have been found, which allow one to define the key characteristics of impact process.

Modeling of Revolute Joints in Topology Optimization of Flexible Multibody Systems

In recent years, topology optimization has been used for optimizing members of flexible multibody systems to enhance their performance. Here, an extension to existing topology optimization schemes for flexible multibody systems is presented in which a more accurate model of revolute joints and bearing domains is included. This extension is of special interest since a connection between flexible members in a multibody system using revolute joints is seen in many applications. Moreover, the modeling accuracy of the bearing area is shown to be influential on the shape of the optimized structure. In this work, the flexible bodies are incorporated in the multibody simulation using the floating frame of reference formulation, and their elastic deformation is approximated using global shape functions calculated in the model order reduction analysis. The modeling of revolute joints using Hertzian contact law is incorporated in this framework by introducing a corrector load in the bearing model. Furthermore, an application example of a flexible multibody system with revolute joints is optimized for minimum value of compliance, and a comparative study of the optimization result is performed with an equivalent system which is modeled with nonlinear finite elements.

Site-Specific Quantification of Bone Quality Using Highly Nonlinear Solitary Waves

Osteoporosis is a well recognized problem affecting millions of individuals worldwide. The ability to diagnose problems in an effective, efficient, and affordable manner and identify individuals at risk is essential. Site-specific assessment of bone mechanical properties is necessary, not only in the process of fracture risk assessment, but may also be desirable for other applications, such as making intraoperative decisions during spine and joint replacement surgeries. The present study evaluates the use of a one-dimensional granular crystal sensor to measure the elastic properties of bone at selected locations via direct mechanical contact. The granular crystal is composed of a tightly packed chain of particles that interact according to the Hertzian contact law. Such chains represent one of the simplest systems to generate and propagate highly nonlinear acoustic signals in the form of compact solitary waves. First, we investigated the sensitivity of the sensor to known variations in bone density using a synthetic cancellous bone substitute, representing clinical bone quality ranging from healthy to osteoporotic. Once the relationship between the signal response and known bone properties was established, the sensor was used to assess the bone quality of ten human cadaveric specimens. The efficacy and accuracy of the sensor was then investigated by comparing the sensor measurements with the bone mineral density (BMD) obtained using dual-energy x-ray absorptiometry (DEXA). The results indicate that the proposed technique is capable of detecting differences in bone quality. The ability to measure site-specific properties without exposure to radiation has the potential to be further developed for clinical applications.

Comparison of Analytical and Experimental Results for Longitudinal Impacts on Elastic Rods

In this paper, the dynamic problem of a rigid body colliding with an elastic rod is studied in some detail. Different contact theories for modeling impact responses are compared with experimental measurements. Based on an idea originally presented by Sears for collisions of two rods with rounded ends, a boundary approach combining Hertzian contact law and St. Venant's elastodynamics is developed to describe longitudinal waves in rods. It is shown that this boundary approach agrees very well with experimental results. For the simulation of long-term dynamic behavior after impact, a traditional rigid-body approach is advantageous because the elastic vibration of the rod will decay fast due to the structural damping and the elastic rod then moves like a rigid body. Hence, for modeling longitudinal impacts, it is suggested that both elastodynamics and rigid-body dynamics are combined into a two-timescale model. The short time behavior of wave propagation due to impacts is modeled using elastodynamics, and the state of the rigid-body mode is transferred to the rigid-body approach as the initial condition for the motion. The long-term behavior after impact is then computed using the rigid-body approach.

Nonlinear Impact Analysis of Laminated Cylindrical and Doubly Curved Shells

The nonlinear impact response of laminated composite cylindrical and doubly curved shells is analyzed using a modified Hertzian contact law. A finite element model is developed based on Sander's shell theory and includes shear deformation effects and nonlinearity due to large deflection. A nine noded isoparametric quadrilateral element is used to model the curved shell. The nonlinear time dependent equations are solved using an iterative scheme and Newmark's method. Numerical results for the contact force and center deflection histories are presented for various impactor conditions, shell geometry and boundary conditions.