scholarly journals AutoMat: automatic differentiation for generalized standard materials on GPUs

2021 ◽  
Author(s):  
Johannes Blühdorn ◽  
Nicolas R. Gauger ◽  
Matthias Kabel
Keyword(s):  
Automatic Differentiation ◽  
Implementation Process ◽  
Integration Scheme ◽  
Universal Method ◽  
Reverse Mode ◽  
Implementation Effort ◽  
Numerical Integration Scheme ◽  
Generalized Standard Materials ◽  
Homogenization Scheme ◽  
Solution Accuracy

AbstractWe propose a universal method for the evaluation of generalized standard materials that greatly simplifies the material law implementation process. By means of automatic differentiation and a numerical integration scheme, AutoMat reduces the implementation effort to two potential functions. By moving AutoMat to the GPU, we close the performance gap to conventional evaluation routines and demonstrate in detail that the expression level reverse mode of automatic differentiation as well as its extension to second order derivatives can be applied inside CUDA kernels. We underline the effectiveness and the applicability of AutoMat by integrating it into the FFT-based homogenization scheme of Moulinec and Suquet and discuss the benefits of using AutoMat with respect to runtime and solution accuracy for an elasto-viscoplastic example.

On the Use of the Automatic Differentiation for Developing a Linear Harmonic Solver

2018 ◽  
Author(s):  
Wei Zhang ◽  
Dingxi Wang ◽  
Xiuquan Huang ◽  
Tianxiao Yang ◽  
Hong Yan ◽  
...  
Keyword(s):  
Harmonic Balance ◽  
Automatic Differentiation ◽  
Harmonic Balance Method ◽  
Source Codes ◽  
Reverse Mode ◽  
Frequency Domain Methods ◽  
The Cost ◽  
Time Periodic ◽  
Small Disturbances

The linear and nonlinear harmonic methods are efficient frequency domain methods for analyzing time periodic unsteady flow fields. They have been widely used in both academia and industry. But the cost and complexity of developing a linear harmonic solver has been limiting its wider applications. On the other hand, the automatic differentiation (AD) has long been used in the CFD community with a focus on generating adjoint codes in a reverse mode. All those AD tools can do a much better job in generating linearized codes in a tangent mode, but so far very little, if any, attention is paid to using AD for developing linear harmonic solvers. The linear harmonic method, in comparison with the harmonic balance method, has its own advantages. For example, it can capture small disturbances very effectively, and avoids aliasing errors which can lead to solution instability since each wave component is solved for separately. This paper presents the effort of using an AD tool to generate major source codes for the development of a linear harmonic solver for analyzing time periodic unsteady flows. It includes the procedures and advice of using AD for such a purpose. A case study is also presented to validate the developed linear harmonic solver.

Dynamic Analysis of Shipping Cask Subjected to Sequential Bolt Preload and Impact Loads

2009 ◽  
Author(s):  
Tsu-te Wu
Keyword(s):  
Finite Element ◽  
Dynamic Analysis ◽  
Numerical Integration ◽  
Dynamic Responses ◽  
Integration Scheme ◽  
Impact Loads ◽  
Element Mesh ◽  
Bolt Preload ◽  
Numerical Integration Scheme ◽  
Structural Responses

This paper presents an improved methodology for evaluating the dynamic responses of shipping casks subjected to the sequential HAC impact loads. The methodology utilizes the import technique of the finite-element mesh and the analytical results form one dynamic analysis using explicit numerical integration scheme into another dynamic analysis also using explicit numerical integration scheme. The new methodology presented herein has several advantages over conventional methods. An example problem is analyzed to illustrate the application of the present methodology in evaluating the structural responses of a shipping cask to the sequential HAC loading.

Modeling of three-dimensional beam nonlinear vibrations generalizing Hencky’s ideas

2022 ◽  
pp. 108128652110679
Author(s):  
Emilio Turco
Keyword(s):  
Kinetic Energy ◽  
Strain Energy ◽  
Nonlinear Vibrations ◽  
Three Dimensional ◽  
Integration Scheme ◽  
Beam Model ◽  
Model Formulation ◽  
Discrete Approach ◽  
Numerical Integration Scheme ◽  
Proposed Model

In this contribution, a novel nonlinear micropolar beam model suitable for metamaterials design in a dynamics framework is presented and discussed. The beam model is formulated following a completely discrete approach and it is fully defined by its Lagrangian, i.e., by the kinetic energy and by the potential of conservative forces. Differently from Hencky’s seminal work, which considers only flexibility to compute the buckling load for rectilinear and planar Euler–Bernoulli beams, the proposed model is fully three-dimensional and considers both the extensional and shear deformability contributions to the strain energy and translational and rotational kinetic energy terms. After having introduced the model formulation, some simulations obtained with a numerical integration scheme are presented to show the capabilities of the proposed beam model.

Insights from Experimental Research on Distributed Channel Assignment in Wireless Testbeds

2012 ◽  
pp. 1443-1460
Author(s):  
Felix Juraschek ◽  
Mesut Günes ◽  
Matthias Philipp ◽  
Bastian Blywis
Keyword(s):  
Operating Systems ◽  
Experimental Research ◽  
Channel Assignment ◽  
Implementation Process ◽  
Channel Characteristics ◽  
Wireless Mesh ◽  
Implementation Effort ◽  
Important Input ◽  
Interference Models

This article presents the DES-Chan framework for experimental research on distributed channel assignment algorithms in wireless mesh testbeds. The implementation process of channel assignment algorithms is a difficult task for the researcher since common operating systems do not support channel assignment algorithms. DES-Chan provides a set of common services required by distributed channel assignment algorithms and eases the implementation effort. The results of experiments to measure the channel characteristics in terms of intra-path and inter-path interference according to the channel distance on the DES-Testbed are also presented. The DES-Testbed is a multi-radio WMN with more than 100 nodes located on the campus of the Freie Universität Berlin. These measurements are an important input to validate common assumptions of WMNs and derive more realistic, measurement-based interference models in contrast to simplified heuristics.

The Effects of Main-Flow Radial Velocity on the Stability of Developing Laminar Pipe Flow

1976 ◽  
Vol 43 (2) ◽  
pp. 209-212 ◽  
Author(s):  
F. C. T. Shen ◽  
T. S. Chen ◽  
L. M. Huang
Keyword(s):  
Radial Velocity ◽  
Main Flow ◽  
Integration Scheme ◽  
Neutral Stability ◽  
Radial Velocity Component ◽  
Numerical Integration Scheme ◽  
Critical Reynolds Numbers ◽  
The Stability ◽  
Direct Numerical Integration ◽  
Sommerfeld Equation

In studying the stability due to axisymmetric disturbances of the developing flow of an incompressible fluid in the entrance region of a circular tube, a generalized version of the Orr-Sommerfeld equation was derived which takes account of the radial velocity component in the main flow. The new terms in the generalized Orr-Sommerfeld equation are inversely proportional to the Reynolds number. The resulting eigenvalue problem consisting of the disturbance equation and the boundary conditions was solved by a direct numerical integration scheme along with an iteration procedure. Neutral stability curves and critical Reynolds numbers at various axial locations are presented. A comparison of the present results with those from the conventional Orr-Sommerfeld equation in which the effect of the main-flow radial velocity is neglected, shows that inclusion of the radial velocity contributes to a destabilization of the main flow.

ANALYTICAL APPROXIMATE SOLUTIONS TO LARGE-AMPLITUDE FREE VIBRATIONS OF UNIFORM BEAMS ON PASTERNAK FOUNDATION

2014 ◽  
Vol 06 (06) ◽  
pp. 1450075 ◽  
Author(s):  
YONGPING YU ◽  
BAISHENG WU
Keyword(s):  
Large Amplitude ◽  
Approximate Solutions ◽  
Free Vibrations ◽  
Integration Scheme ◽  
Nonlinear Frequency ◽  
Pasternak Foundation ◽  
Analytical Approximations ◽  
Numerical Integration Scheme ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration

This paper is concerned with the large-amplitude vibration behavior of simply supported and clamped uniform beams, with axially immovable ends, on Pasternak foundation. The combination of Newton's method and harmonic balance one is used to deal with these vibrations. Explicit and brief analytical approximations to nonlinear frequency and periodic solution of the beams for various values of the two stiffness parameters of the Pasternak foundation, small as well as large amplitudes of oscillation are presented. The analytical approximate results show excellent agreement with those from numerical integration scheme. Due to brevity of expressions, the present analytical approximate solutions are convenient to investigate effects of various parameters on the large-amplitude vibration response of the beams.

Inelastic, Nonlinear Analysis of Stiffened Shells of Revolution by Numerical Integration

1974 ◽  
Vol 96 (2) ◽  
pp. 121-130 ◽  
Author(s):  
H. S. Levine ◽  
V. Svalbonas
Keyword(s):  
Numerical Integration ◽  
Cross Sections ◽  
Thermal Loading ◽  
Large Deflection ◽  
Kinematic Hardening ◽  
Integration Scheme ◽  
Shells Of Revolution ◽  
Stiffened Shells ◽  
Numerical Integration Scheme ◽  
Deflection Analysis

This paper describes the latest addition to the STARS system of computer programs, STARS-2P, for the plastic, large deflection analysis of axisymmetrically loaded shells of revolution. The STARS system uses a numerical integration scheme to solve the governing differential equations. Several unique features for shell of revolution programs that are included in the STARS-2P program are described. These include orthotropic nonlinear kinematic hardening theory, a variety of shell wall cross sections and discrete ring stiffeners, cyclic and nonproportional mechanical and thermal loading capability, the coupled axisymmetric large deflection elasto-plastic torsion problem, an extensive restart option, arbitrary branching capability, and the provision for the inelastic treatment of smeared stiffeners, isogrid, and waffle wall constructions. To affirm the validity of the results, comparisons with available theoretical and experimental data are presented.

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