A numerical investigation on impulse-induced nonlinear longitudinal waves in pantographic beams

This contribution presents the results of a campaign of numerical simulations aimed at better understanding the propagation of longitudinal waves in pantographic beams within the large-deformation regime. Initially, we recall the key features of a Lagrangian discrete spring model, which was introduced in previous works and that was tested extensively as capable of accurately forecasting the mechanical response of structures based on the pantographic motif, both in statics and dynamics. Successively, a stepwise integration scheme used to solve equations of motions is briefly discussed. The key content of the present contribution concerns the thorough presentation of some selected numerical simulations, which focus in particular on the propagation of stretch profiles induced by impulsive loads. The study takes into account different tests, by varying the number of unit cells, i.e., the total length of the system, spring stiffnesses, the shape of the impulse, as well as its properties such as duration and peak amplitude, and boundary conditions. Some conjectures about the form of traveling waves are formulated, to be confirmed by both further numerical simulations and analytical investigations.

Dynamic Stability of Sandwich Beams/Wide Plates Subjected to Axial Impulsive Loads

This paper presents an analysis for the dynamic stability of sandwich beams/wide plates subjected to axial impulsive loads. The formulation and solution of the problem is done by use of the extended high-order sandwich panel theory (EHSAPT). With the initial geometric imperfection included, the equations of motion in terms of seven generalized displacements are derived. The dynamic response of sandwich panels subjected to three different types of impulsive loads, namely, step, linear decay, and triangular impulse, is studied. Furthermore, the effects of the oscillation mode number, face/core materials, and geometries are investigated. It is observed that all measurements of the dynamic response, such as the maximum displacements, strains, and stresses, change at the same rate as the change of the impulse load magnitude and duration, for a specific impulse load profile. When the impulse load is lower than the static buckling load, the dynamic response is bounded no matter how long the load is applied. A step impulsive axial load with magnitude lower than the static buckling load can lead a sandwich panel to have a dynamic response as high as twice the static response. When the impulse load is higher than the static critical load, the dynamic response is unbounded with increasing load duration. However, it is possible that the dynamic response can be controlled at a low level if the duration of the impulse load is short enough, and thus, in this case, the load can safely exceed the static critical load.

On the experimental testing procedures for ultra-high molecular weight polyethylene (UHMWPE) behaviour evaluation in static and dynamic regime

Over the past decade, extensive work has been carried out on the study of materials behaviour subjected to a variety type of loads, especially on new materials with improved mechanicals properties. The UHMWPE, ultra-high molecular weight polyethylene, a material with hight resistance at static, dynamic and even impulsive loads that can have a large number of practical applications is proposed to be studied in this article. The current paper aims to propose a series of experimental procedures in order to characterise the behaviour of different specimen types of ultra-high molecular weight polyethylene subjected to static and dynamic loads. Laboratory tests were performed aiming to confirm the proposed experimental approach.

Enhanced Single-Degree-of-Freedom Analysis of Thin Elastic Plates Subjected to Blast Loading Using an Energy-Based Approach

Single-degree-of-freedom (SDOF) models are known to represent a valid tool in support of design. Key assumptions of these models, on the other hand, can strongly affect the expected predictions, hence resulting in possible overconservative or misleading estimates for the response of real structural systems under extreme actions. Among others, the description of the input loads can be responsible for major design issues, thus requiring the use of more refined approaches. In this paper, a SDOF model is developed for thin elastic plates under large displacements. Based on the energy approach, careful attention is given for the derivation of the governing linear and nonlinear parameters, under different boundary conditions of technical interest. In doing so, the efforts are dedicated to the description of the incoming blast waves. In place of simplified sinusoidal pressures, the input impulsive loads are described with the support of infinite trigonometric series that are more accurate. The so-developed SDOF model is therefore validated, based on selected literature results, by analyzing the large displacement response of thin elastic plates, under several boundary conditions and real blast pressures. Major advantage for the validation of the proposed SDOF model is obtained from experimental finite element (FE) and finite difference (FD) models of literature, giving evidence of a rather good correlation and confirming the validity of the presented formulation.

Stepwise analysis of pantographic beams subjected to impulsive loads

Materials based on pantographic unit cells have very interesting mechanical peculiarities. For these reasons they are largely studied from a theoretical, experimental, and numerical point of view. Numerical simulations furnish an important contribution for the the design and optimization of such materials and, more generally, for metamaterials. Here, we consider the influence of inertial forces, removing the hypothesis of quasistatic loading. By using an intrinsically discrete model, inspired by Hencky’s ideas, already tested in a series of published works, here we add the contribution of inertial forces and, in the framework of stepwise schemes, we re-experience an adaptive integration scheme capable of reconstructing the best structural response corresponding to a prefixed time step. Several numerical simulations, although preparatory, inspire some remarks on materials based on pantographic cells and outline the way for future challenges.