Abstract

Abstract

In materials with a strain‐softening characteristic behavior, classical continuum mechanics favors uncontrolled strain localization in numerical analyses. Several methods have been proposed to regularize the problem. Two such localization limiters developed to overcome spurious instabilities in computational failure analysis are examined and compared. A disturbance analysis, on both models, is performed to obtain the closed‐form solution of propagating wave velocities as well as the velocities at which the energy travels. It also shows that in spite of forcing the same stress‐strain response, the wave equation does not yield similar results. Both propagations of waves are dispersive, but the internal length of each model is different when equivalent behavior is desired. In fact, the previously suggested derivations of gradient models from nonlocal integral models were not completely rigorous. The perturbation analysis is pursued in the discrete space where computations are done, and the closed form solutions are also obtained. The finite‐element discretization introduces an added dispersion associated to the regularization technique. Therefore, the influence of the discretization on the localization limiters can be evaluated. The element size must be smaller than the internal length of the models in order to obtain sufficient accuracy.

Abstract

Three Galerkin methods-continuous Galerkin, Compact Discontinuous Galerkin, and hybridizable discontinuous Galerkin-are compared in terms of performance and computational efficiency in 2-D scattering problems for low and high-order polynomial approximations. The total number of DOFs and the total runtime are used for this correlation as well as the corresponding precision. The comparison is carried out through various numerical examples. The superior performance of high-order elements is shown. At the same time, similar capabilities are shown for continuous Galerkin and hybridizable discontinuous Galerkin, when high-order elements are adopted, both of them clearly outperforming compact discontinuous Galerkin. hree Galerkin methods—continuous Galerkin, Compact Discontinuous Galerkin, and hybridizable discontinuous Galerkin—are compared in terms of performance and computational efficiency in 2-D scattering problems for low and high-order polynomial approximations. The total number of DOFs and the total runtime are used for this correlation as well as the corresponding precision. The comparison is carried out through various numerical examples. The superior performance of high-order elements is shown. At the same time, similar capabilities are shown for continuous Galerkin and hybridizable discontinuous Galerkin, when high-order elements are adopted, both of them clearly outperforming compact discontinuous Galerkin

Abstract

Solving the Helmholtz equation for a large number of input data in an heterogeneous media and unbounded domain still represents a challenge. This is due to the particular nature of the Helmholtz operator and the sensibility of the solution to small variations of the data. Here a reduced order model is used to determine the scattered solution everywhere in the domain for any incoming wave direction and frequency. Moreover, this is applied to a real engineering problem: water agitation inside real harbors for low to mid-high frequencies. The Proper Generalized Decomposition (PGD) model reduction approach is used to obtain a separable representation of the solution at any point and for any incoming wave direction and frequency. Here, its applicability to such a problem is discussed and demonstrated. More precisely, the contributions of the paper include the PGD implementation into a Perfectly Matched Layer framework to model the unbounded domain, and the separability of the operator which is addressed here using an efficient higher-order projection scheme. Then, the performance of the PGD in this framework is discussed and improved using the higher-order projection and a Petrov-Galerkin approach to construct the separated basis. Moreover, the efficiency of the higherorder projection scheme is demonstrated and compared with the higher-order singular value decomposition.

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Abstract

This paper is concerned with the inverse dynamics of flexible mechanical systems whose motion is governed by quasi-linear hyperbolic partial differential equations. Problems that appear by applying classical solution strategies to the problem at hand, e.g. integrating the problem at hand sequentially in space and time will be adressed in this work. Motivated by the hyperbolic structure of the underlying initial boundary value problem, two methods that are based on a simultaneous space-time integration will be presented. Special emphasize will be given to the phenomena of wave propagation within geometrically exact beams and its relevance regarding the inverse dynamics problem.

Abstract

The "System for Predicting the Operation of Unmanned Aerial Vehicles on Naval Platforms" (SPOVENT) project aims to determine the studies and developments necessary to obtain and characterise the data required to predict ship movements in waves in real time and, therefore, to be able to predict the optimum windows for recovering/landing UAVs. The project was developed in two phases: the objective of the first one was the identification of the available technology applicable to the prediction of the 3D vessel motions during its operation plus the determination of maximum vessel motion limits in order to carry out the capture of UAVs in safe conditions; then came the development of two algorithms to predict the movements of the vessel depending on the waves that it will encounter during its navigation. After the completion of these initial phases, the validation and evaluation of the algorithms developed is carried out, followed by the development of the SPOVENT demonstrator, implementing the algorithm with best results. To determine the algorithm which best predicts the time windows in which the UAV will be able to operate, the following evaluation and validation criteria are established: accuracy of the prediction of the operation windows, range of application, input data required for its correct operation, possibility of adaptation to different types of vessels and required calculation time. Once the algorithm to be implemented in the demonstrator has been selected, a computer application is developed that shows the user the time windows to perform these operations with adequate safety. The design of the application ensures that user intervention is minimal, considering the operating conditions on a ship, including easy-to-read indicators and easily accessible buttons. Additionally, the demonstrator will be a tool to evaluate the operational criteria (STANAG) of different missions during navigation, by means of the ship's movement variables registered by an IMU sensor

Abstract

Metamaterials with engineered microstructures exhibit exceptional properties such as negative Poisson’s ratio, energy absorption, and bandgap. These materials can prevent propagation of elastic waves in certain range of frequency called bandgap. The microstructure of these materials affects the overall response of the structures. Microstructures may undergo significant rotations and their rotary inertia needs to be considered along with deformation. As the metamaterials in the study involve cracks, we develop a finite deformation micropolar peridynamics (PD) theory. The proposed PD micropolar theory is validated by comparing the results obtained from the boundary element solutions of plate with a hole. The response of metamaterials with periodic arrangement of holes and cracks is studied under static and dynamic loads and the results are compared with the nonpolar PD theory.

Abstract