Numerical Dispersion Error in Finite Methods, Exemplified by the Perfectly Straight Beam Undergoing Bending Oscillations

In chapter (1) we present numerical simulations of the eigenstates of a MBS-model (Multi-Body-System) for a continuous ring structure. Both eigenfrequencies and eigenforms show a systematic error for high mode numbers. In order to understand the source of this error, in chapter (2) we calculate analytical solutions for the eigenfrequencies of a MBS- and a FEM-model (Finite-Element-Method) for the straight beam undergoing bending oscillations. We summarize our results in chapter (3)

Analysis and Numerical Approximation of an Integro-differential Equation Modeling Non-local Effects in Linear Elasticity

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Long-range interactions for linearly elastic media resulting in nonlinear dispersion relations are modeled by an initial-value problem for an integro-differential equation (IDE) that incorporates non-local effects. Interpreting this IDE as an evolutionary equation of second order, well-posedness in L ∞(ℝ) as well as jump relations are proved. Moreover, the construction of the micromodulus function from the dispersion relation is studied. A numerical approximation based upon quadrature is suggested and carried out for two examples, one involving jump discontinuities in the initial data corresponding to a Riemann-like problem

The Cauchy Problem for a One Dimensional Nonlinear Peridynamic Model

This paper studies the Cauchy problem for a one-dimensional nonlinear peridynamic model describing the dynamic response of an infinitely long elastic bar. The issues of local well-posedness and smoothness of the solutions are discussed. The existence of a global solution is proved first in the sublinear case and then for nonlinearities of degree at most three. The conditions for finite-time blow-up of solutions are established.Comment: To appear in Journal of Differential Equations (added references, corrected typos, minor revision in Section 2, 18 pages

The Cauchy Problem for a One Dimensional Nonlinear Peridynamic Model

This paper studies the Cauchy problem for a one-dimensional nonlinear peridynamic model describing the dynamic response of an infinitely long elastic bar. The issues of local well-posedness and smoothness of the solutions are discussed. The existence of a global solution is proved first in the sublinear case and then for nonlinearities of degree at most three. The conditions for finite-time blow-up of solutions are established.Comment: To appear in Journal of Differential Equations (added references, corrected typos, minor revision in Section 2, 18 pages

Crack nucleation in a peridynamic solid

A condition for the emergence of a discontinuity in an elastic peridynamic body is proposed, resulting in a material stability condition for crack nucleation. The condition is derived by determining whether a small discontinuity in displacement, superposed on a possibly large deformation, grows over time. Stability is shown to be determined by the sign of the eigenvalues of a tensor field that depends only on the linearized material properties. This condition for nucleation of a discontinuity in displacement can be interpreted in terms of the dynamic stability of plane waves with very short wavelength. A numerical example illustrates that cracks in a peridynamic body form spontaneously as the body is loaded

Analysis and numerical approximation of an integro-differential equation modelling non-local effects in linear elasticity

Long-range interactions for linearly elastic media resulting in nonlinear dispersion relations are modelled by an initial-value problem for an integro-differential equation (IDE) that incorporates non-local effects. Interpreting this IDE as an evolutionary equation of second order, well-posedness in L^{\infty}(\rz) as well as jump relations are proved. A numerical approximation based upon quadrature is suggested and carried out for two examples, one involving jump discontinuities in the initial data corresponding to a Riemann-like problem

A Sophisticated Environment for Protocol Simulation and Testing

This paper describes a protocol development environment aimed at simplifying the development and testing of communication protocols. Protocols are defined in the development environment in a specification language, called BDL, which is based on the process algebra CCS. The behavior of a system is thus expressed in terms of communicating processes, and a rich set of analytical theories for verification are available. The BDL language and the simulator for the language are outlined in the paper. The interactive user interface, implemented on a graphical workstation, is presented. Further the paper describes an interface to the development environment which allows the simulator to interact with protocol implementations directly, and therefore enables protocol testing based on formal definitions

Determination of Ballistic Limit for IM7/8552 Using Peridynamics

Significant testing is required to design and certify primary aircraft structure subject to High Energy Dynamic Impact (HEDI) events; current work under the NASA Advanced Composites Consortium (ACC) HEDI Project seeks to determine the state-of-the-art of dynamic fracture simulations for composite structures in these events. This paper discusses one of four Progressive Damage Analysis (PDA) methods selected for this project: peridynamics, through EMU implementation. A brief discussion of peridynamic theory is provided, followed by an outline of ballistic impact testing performed for model development and assessment. Detailed modeling approach and test-analysis correlation for a single open test case are presented, followed by the results of a series of blind predictions made prior to testing and test-analysis correlation performed with measured NASA test results. Specifically, we present simulation results for the ballistic limit (V50) of IM7/8552 composite panels ballistically tested with an impactor representative of a high-velocity fan-blade-out condition. In particular, force and displacement history and the damage state determined analytically are compared to measured results. Ultimately, peridynamics has the ability to predict damage patterns, impact force and deflections during a high energy dynamic impact event on composite panels of different layups using two different types of impactors. Blind predictions were promising and increased confidence in the model for impact simulation. There are open questions regarding the fidelity of the test fixture idealization in regards to stiffness and damping which will need to be addressed in future work

EFEITO DA APLICAÇÃO DE BIOFERTILIZANTES À BASE DE ESTERCO BOVINO FRESCO NO CRESCIMENTO DE PIMENTA DE CHEIRO (Capsicum Chinense Jacq.)

No Brasil o cultivo de pimenta é de grande importância tanto pela característica da rentabilidade, quando o produtor agrega valor ao produto, quanto pela importância social. Nesse sentido, o presente trabalho objetivou-se avaliar os efeitos das propostas de biofertilizantes à base de esterco bovino fresco no crescimento e produtividade das mudas de pimenta de cheiro. O delineamento experimental utilizado foi em blocos casualizados, com cinco tratamentos e quatro repetições, cuja os tratamentos foram: 1) testemunha, sem aplicação de biofertilizante; 2) biofertilizante puro, composto com 100% de esterco bovino fresco; 3) biofertilizante composto com 75% de esterco bovino fresco + 25% de caroço de açaí fresco triturado; 4) biofertilizante composto com 50% de esterco bovino fresco + 50% de caroço de açaí fresco triturado e; 5) biofertilizante composto com 25% de esterco bovino fresco + 75% de caroço de açaí fresco triturado. Os dados coletados foram submetidos à análise de variância (teste F), e teste Tukey ao nível de 5% de probabilidade, no programa estatístico (Assistat versão 7.7 beta). Dentre os tratamentos testados, o tratamento 02 composto pelo biofertilizante à base de esterco bovino fresco promoveu o maior crescimento e desenvolvimento para as plantas.