Two Efficient Time-Marching Explicit Procedures Considering Spatially/Temporally-Defined Adaptive Time-Integrators

2021 ◽  
pp. 2150051
Author(s):  
Delfim Soares
Keyword(s):  
Degrees Of Freedom ◽  
Numerical Results ◽  
Spatial Discretization ◽  
Adaptive Procedure ◽  
Excellent Performance ◽  
Time Integrators ◽  
Time Marching ◽  
Adaptive Time ◽  
Discretization Technique ◽  
Discretized Model

In this paper, two explicit time-marching techniques are discussed for the solution of hyperbolic models, which are based on adaptively computed parameters. In both these techniques, time integrators are locally and automatically evaluated, taking into account the properties of the spatially/temporally discretized model and the evolution of the computed responses. Thus, very versatile solution techniques are enabled, which allows computing highly accurate responses. Here, the so-called adaptive [Formula: see text] method is formulated based on the elements of the adopted spatial discretization (elemental formulation), whereas the so-called adaptive [Formula: see text] method is formulated based on the degrees of freedom of the discretized model (nodal formulation). In this context, each adaptive procedure can be better applied according to the specific features of the focused spatial discretization technique. At the end of the paper, numerical results are presented, illustrating the excellent performance of the discussed adaptive formulations.

An Optimized Explicit–Implicit Time-Marching Formulation for Dynamic Analysis

2020 ◽  
pp. 2050045
Author(s):  
Delfim Soares ◽  
Matheus M. Rodrigues
Keyword(s):  
Dynamic Analysis ◽  
Time Domain ◽  
Optimization Algorithm ◽  
Computational Efficiency ◽  
Implicit Time ◽  
Excellent Performance ◽  
Time Step ◽  
Time Marching ◽  
Adaptive Time

In this paper, an optimized approach is proposed to enhance the performance of combined explicit–implicit time-domain analyses. In this context, an entirely automated explicit-implicit adaptive time-marching procedure is discussed as well as an optimization algorithm is introduced to compute the adopted time-step value of the analysis, so that the amount of explicit and implicit elements occurring along the model may be optimally provided, in terms of computational efficiency. The proposed formulation is very effective, allowing evaluating highly accurate responses considering much reduced computational efforts. At the end of the manuscript, numerical applications are presented, illustrating the excellent performance of the proposed formulation.

scholarly journals A Weighted-Least-Squares Meshless Model for Non-Hydrostatic Shallow Water Waves

Water ◽  
2021 ◽  
Vol 13 (22) ◽  
pp. 3195
Author(s):  
Nan-Jing Wu ◽  
Yin-Ming Su ◽  
Shih-Chun Hsiao ◽  
Shin-Jye Liang ◽  
Tai-Wen Hsu
Keyword(s):  
Least Squares ◽  
Shallow Water ◽  
Water Waves ◽  
Dynamic Pressure ◽  
Weighted Least Squares ◽  
Shallow Water Equation ◽  
Analytic Solutions ◽  
Numerical Results ◽  
Benchmark Problems ◽  
Time Marching

In this paper, an explicit time marching procedure for solving the non-hydrostatic shallow water equation (SWE) problems is developed. The procedure includes a process of prediction and several iterations of correction. In these processes, it is essential to accurately calculate the spatial derives of the physical quantities such as the temporal water depth, the average velocities in the horizontal and vertical directions, and the dynamic pressure at the bottom. The weighted-least-squares (WLS) meshless method is employed to calculate these spatial derivatives. Though the non-hydrostatic shallow water equations are two dimensional, on the focus of presenting this new time marching approach, we just use one dimensional benchmark problems to validate and demonstrate the stability and accuracy of the present model. Good agreements are found in the comparing the present numerical results with analytic solutions, experiment data, or other numerical results.

Transverse Vibrations of Cantilever Beams Having Unequal Breadth and Depth Tapers

1977 ◽  
Vol 44 (4) ◽  
pp. 737-742 ◽  
Author(s):  
B. Downs
Keyword(s):  
Stress Distribution ◽  
Cross Section ◽  
Degrees Of Freedom ◽  
Dynamic Behaviour ◽  
Natural Frequencies ◽  
Distribution Patterns ◽  
Continuous Systems ◽  
Cantilever Beams ◽  
Transverse Vibrations ◽  
Discretization Technique

Natural frequencies of doubly symmetric cross section, isotropic cantilever beams, based on both Euler and Timoshenko theories, are presented for 36 combinations of linear depth and breadth taper. Results obtained by a new dynamic discretization technique include the first eight frequencies for all geometries and the stress distribution patterns for the first four (six) modes in the case of the wedge. Comparisons are drawn wherever possible with exact solutions and with other numerical results appearing in the literature. The results display outstanding accuracy and demonstrate that it is possible to model with high precision the dynamic behaviour of continuous systems by discretization on to a strictly limited number of degrees of freedom.

Best Structural Theories for Free Vibrations of Sandwich Composites via Machine Learning

2019 ◽  
Author(s):  
Marco Petrolo ◽  
Erasmo Carrera
Keyword(s):  
Degrees Of Freedom ◽  
Computational Cost ◽  
Free Vibrations ◽  
Numerical Results ◽  
Design Parameters ◽  
Sandwich Composites ◽  
Accuracy Requirement ◽  
Minimum Number ◽  
Carrera Unified Formulation ◽  
Structural Theories

Abstract This work presents a novel methodology for the development of refined structural theories for the modal analysis of sandwich composites. Such a methodology combines three well-established techniques, namely, the Carrera Unified Formulation (CUF), the Axiomatic/Asymptotic Method (AAM), and Artificial Neural Networks (NN). CUF generates structural theories and finite element arrays hierarchically. CUF provides the training set for the NN in which the structural theories are inputs and the natural frequencies targets. AAM evaluates the influence of each generalized displacement variable, and NN provides Best Theory Diagrams (BTD), i.e., curves providing the minimum number of nodal degrees of freedom required to satisfy a given accuracy requirement. The aim is to build BTD with far less computational cost than in previous works. The numerical results consider sandwich spherical shells with soft cores and different features, such as thickness and curvature to investigate their influence on the choice of generalized displacement variables. The numerical results show the importance of third-order generalized displacement variables and prove that the present framework can be of interest to evaluate the performance of any structural theory as typical design parameters change and provide guidelines to the analysts on the most convenient computational model to save computational cost without accuracy penalties.

scholarly journals Inconsistent Stability of Newmark's Method in Structural Dynamics Applications

2015 ◽  
Vol 10 (5) ◽  
Author(s):  
Richard Wiebe ◽  
Ilinca Stanciulescu
Keyword(s):  
Structural Dynamics ◽  
Finite Element Models ◽  
Interesting Phenomenon ◽  
Physical Systems ◽  
Stiffness Matrices ◽  
Time Integrators ◽  
Direct Interpretation ◽  
Time Marching ◽  
The Stability ◽  
Marching Scheme

The stability of numerical time integrators, and of the physical systems to which they are applied, are normally studied independently. This conceals a very interesting phenomenon, here termed inconsistent stability, wherein a numerical time marching scheme predicts a stable response about an equilibrium configuration that is, in fact, unstable. In this paper, time integrator parameters leading to possible inconsistent stability are first found analytically for conservative systems (symmetric tangent stiffness matrices), then several structural arches with increasing complexity are used as numerical case studies. The intention of this work is to highlight the potential for this unexpected, and mostly unknown, behavior to researchers studying complex dynamical systems, especially through time marching of finite element models. To allow for direct interpretation of our results, the work is focused on the Newmark time integrator, which is commonly used in structural dynamics.

Simulation and Optimization of Flexible Hooke Hinge

2012 ◽  
Vol 201-202 ◽  
pp. 574-577 ◽  
Author(s):  
Wei Sun
Keyword(s):  
Degrees Of Freedom ◽  
Large Deflection ◽  
Compliant Mechanisms ◽  
Rotation Angle ◽  
Basic Unit ◽  
Excellent Performance ◽  
Simulation And Optimization ◽  
Element Simulation ◽  
New Type ◽  
Perpendicular Axis

Flexible Flexible hinge is a typical flexible element in compliant mechanisms. Hooke hinge is a combination of the two revolute whose axis through the same point. It allows the two components have relative rotation of two degrees of freedom along the perpendicular axis. The distributed multi-reeds and large-deflection flexible Hooke hinge with the curve reed as the basic unit is analysed by finite element simulation, and is optimized in Multi-objective. The Hooke hinge after optimization lines with the basic rotation characteristics of Hooke hinge. It can provide the larger two-dimensional rotating schedule.It’s unilateral rotation angle can up to ±11.9 °, and the center drift and input coupling of rotation is small. So this flexible Hooke hinge is a new type of large deformation flexible Hook hinge which have excellent performance.

Direct Kinematic Singularities of 3-3 Stewart-Gough Platforms

2005 ◽  
Vol 219 (4) ◽  
pp. 311-324 ◽  
Author(s):  
C H Liu ◽  
J Chiu
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Polynomial Equation ◽  
Numerical Results ◽  
Polynomial Equations ◽  
Kinematic Singularity ◽  
Cubic Polynomial ◽  
Singular Configuration ◽  
Kinematic Singularities ◽  
Stewart Gough Platform

In this article, a method to locate direct kinematic singularities of a 3-3 Stewart-Gough parallel manipulator (called a Stewart manipulator henceforth) is proposed. The Stewart manipulator is first replaced by an analogous manipulator, the 3PRPS parallel manipulator, and as the first three active joints of this manipulator remain fixed, this manipulator reduces to an asymmetric 3RPS parallel manipulator. With all moving platform's degrees of freedom, except its height, properly specified, there exists at least one height that gives rise to direct kinematic singularity of the asymmetric 3RPS manipulator and this height is a root of a cubic polynomial equation. The procedure to locate direct kinematic singularities thus reduces to solving cubic polynomial equations. Numerical results show that every singular configuration of the asymmetric 3RPS manipulator thus-determined is also a singular configuration of the 3-3 Stewart-Gough platform.

scholarly journals THE INFLUENCE OF FOUNDATION MASS ON DYNAMIC RESPONSE OF TRACK-VEHICLE INTERACTION

2018 ◽  
Author(s):  
Pham Dinh Trung
Keyword(s):  
Dynamic Response ◽  
Degrees Of Freedom ◽  
Dynamic Balance ◽  
Mass Parameter ◽  
Numerical Results ◽  
Integrated System ◽  
Railway Track ◽  
Moving Vehicle ◽  
Balance Principle ◽  
Foundation Model

The influence of foundation mass on the dynamic response of track-vehicle interaction is studied in this paper. The moving vehicle is modeled as a two-axle mass-spring-damper system having four degrees of freedom. The new foundation model, called “Dynamic foundation model” including linear elastic spring, shear layer, viscous damping and special consideration of foundation mass parameter, is used to analyze dynamic response of the track-vehicle interaction. Then, the railway track on dynamic foundation model subjected to a moving vehicle is regarded as an integrated system. By means of finite element method and dynamic balance principle, the governing equation of motion for railway track-vehicle-foundation interaction is derived and solved by step-by-step integration method. The accuracy of the algorithm is also verified by comparing the numerical results with the other numerical results in the literature. The influence of foundation mass parameter on the dynamic response of railway track-vehicle interaction is investigated. The numerical results show that the foundation mass effects significantly on the dynamic response of track-vehicle interaction and it is more increasing dynamic displacements than others without foundation mass. The study has meaning practice and the foundation quite agrees to describe true behavior of soil in the problems of the analyzing dynamic response of structures on the foundation.

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