Elastic wave dispersion equation considering material and geometric nonlinearities

In this letter, we describe the propagation of longitudinal waves in one-dimensional nonlinear elastic thin rods with material nonlinearity and geometric nonlinearity. Mathematical analysis is used to derive the analytical dispersion relationship of longitudinal waves; subsequently, the numerical Fourier spectrum method is used to solve the nonlinear wave equation directly and the results are used to verify the correctness of the derived nonlinear dispersion relation.

Comparison of nonlinear solution techniques named arc-length for the geometrically nonlinear analysis of structural systems

The nonlinearity issue is one of the promising fields in the engineering area. Particularly, the geometric nonlinearity bears big importance for the structural systems showing a tendency of larger deflection. In order to obtain a correct load-deflection relation for the structural system subjected to any external load, an advanced incremental-iterative based approach has to be utilized in the analysis of nonlinear responses. Arc length method has been proven to be the most perfect one among the nonlinear analysis approaches. Thus, it is extensively applied to the structural systems with pin-connected joints. This study attempts to compare two variations of arc length method named “spherical” and “linearized” for the nonlinear analysis of structural system with rigid-connected joints. Also, two different element formulations are utilized to discretize the structural systems. Two open-source coded programs, Opensees and FEAP, are employed for six benchmark structural systems in order to compare the performance of employed arc-length techniques. Furthermore, in order to make a further observation in the nonlinear behavior of application examples, their simulations are not only sketched using graphs, but also displayed through the movies for each of benchmark tests. Consequently, the linearized type arc length technique implemented in FEAP shows a more success with a better prediction of load-deflection relation, noting that Opensees has a big advantage of having an element, which is capable of simulating the geometric nonlinearity.

A Study of a Pendulum-Like Vibration Isolator With Quasi-Zero-Stiffness

This article introduces a pendulum element to a 3-spring vibration isolator to achieve a high-static-low-dynamic (HSLD) stiffness or even quasi-zero stiffness (QZS) around the equilibrium position. Numerical simulation is given and the harmonic balance method (HBM) is used to obtain time responses for analysis. Effects of different parameters on the isolation performance are studied and summarized. Approximation force and displacement transmissibility of the system are calculated to evaluate the isolation performance. Comparisons are made with those of an equivalent linear isolator and the typical 1 degree-of-freedom (DOF) QZS isolator. Results show that the novel vibration isolator performs better than existing isolators under selected parameters. The left bent backbone of the novel isolator demonstrates evident softening geometric nonlinearity. Therefore, it achieves a wider frequency range of isolation than the linear 1DOF isolator and typical 3-spring QZS isolator. Moreover, the transmissibility of the novel isolator is smaller at higher frequencies as the jump phenomenon occurs on the left.

Topology Optimization using the Discrete Element Method. Part 1: Methodology, Validation, and Geometric Nonlinearity

Structural Topology optimization is attracting increasing attention as a complement to additive manufacturing techniques. The optimization algorithms usually employ continuum-based Finite Element analyses, but some important materials and processes are better described by discrete models, for example granular materials, powder-based 3D printing, or structural collapse. To address these systems, we adapt the established framework of SIMP Topology optimization to address a system modelled with the Discrete Element Method. We consider a typical problem of strain energy minimization, for which we define objective function and related sensitivity for the Discrete Element framework. The method is validated for simply supported beams discretized as interacting particles, whose predicted optimum solutions match those from a classical continuum-based algorithm. A parametric study then highlights the effects of mesh dependence and filtering. An advantage of the Discrete Element Method is that geometric nonlinearity is captured without additional complexity; this is illustrated when changing the beam supports from rollers to hinges, which indeed generates different optimum structures. The proposed Discrete Element Topology Optimization method enables future incorporation of nonlinear interactions, as well discontinuous processes such as during fracture or collapse.

Behavioural Study of Thin Plate Under Large Deflection Theory

For a thin plate, if the deformation is on the order of the thickness and stay elastic, linear theory might not turn out correct results because it does not predict the in plane movement of the member. Therefore, to account for the inconsistencies of geometric nonlinearity, large deflection theory is required [1]. This report pertains to the analytical study dispensed to check the behavior of thin plate under fixed and pinned edge conditions, and for diverse thicknesses, under the small and large deflection theories. The deformation is additionally studied, supported by Von-Karman equations. Non linear analysis has been performed on FE model using the ANSYS software. The consequences of geometric nonlinearities are mentioned. Outline on conclusion of the theoretical and experimental results obtained, are compared so as to review the similarity of the modeling and theory.