Sensitivity Analysis of Beam Cross-Section Stiffness Using Adjoint Method

2017 ◽  
Author(s):  
Alfonso Callejo ◽  
Olivier Bauchau ◽  
Boris Diskin ◽  
Li Wang
Keyword(s):  
Sensitivity Analysis ◽  
Objective Function ◽  
Cross Section ◽  
Structural Parameters ◽  
Flexible Multibody Dynamics ◽  
Numerical Differentiation ◽  
Adjoint Equations ◽  
Design Parameters ◽  
Adjoint Sensitivity ◽  
Cross Sectional

The design optimization of rotorcraft through multidisciplinary aeroelastic models with hundreds of thousands of degrees of freedom requires a computationally efficient sensitivity analysis to obtain the objective function gradient. A fundamental part of rotorcraft analysis is the flexible multibody dynamics solver, which in the current work relies on an accurate three-dimensional representation of the beams. This paper presents the theoretical adjoint sensitivity analysis of the first structural analysis step, namely the computation of cross-sectional properties of the beams in the form of six-dimensional stiffness matrices. The adjoint equations are carefully derived, as are the derivatives of the objective function with respect to the design parameters. The method is then validated by comparing certain design sensitivities of a three-ply, composite cross-section with those obtained through real-step and complex-step numerical differentiation. The presented analysis allows the user to quantify the effect of basic structural parameters on fundamental sectional properties that can later be used in the full dynamic simulation.

Direct Sensitivity Analysis of Spatial Multibody Systems With Joint Friction Using Index-1 Formulation

2021 ◽  
Author(s):  
Adwait Verulkar ◽  
Corina Sandu ◽  
Daniel Dopico ◽  
Adrian Sandu
Keyword(s):  
Sensitivity Analysis ◽  
Dynamic Systems ◽  
Multibody Systems ◽  
Friction Model ◽  
Design Parameters ◽  
Adjoint Sensitivity ◽  
Joint Friction ◽  
Multibody Dynamic ◽  
Model Dynamics ◽  
Direct Sensitivity

Abstract Sensitivity analysis is one of the most prominent gradient based optimization techniques for mechanical systems. Model sensitivities are the derivatives of the generalized coordinates defining the motion of the system in time with respect to the system design parameters. These sensitivities can be calculated using finite differences, but the accuracy and computational inefficiency of this method limits its use. Hence, the methodologies of direct and adjoint sensitivity analysis have gained prominence. Recent research has presented computationally efficient methodologies for both direct and adjoint sensitivity analysis of complex multibody dynamic systems. The contribution of this article is in the development of the mathematical framework for conducting the direct sensitivity analysis of multibody dynamic systems with joint friction using the index-1 formulation. For modeling friction in multibody systems, the Brown and McPhee friction model has been used. This model incorporates the effects of both static and dynamic friction on the model dynamics. A case study has been conducted on a spatial slider-crank mechanism to illustrate the application of this methodology to real-world systems. Using computer models, with and without joint friction, effect of friction on the dynamics and model sensitivities has been demonstrated. The sensitivities of slider velocity have been computed with respect to the design parameters of crank length, rod length, and the parameters defining the friction model. Due to the highly non-linear nature of friction, the model dynamics are more sensitive during the transition phases, where the friction coefficient changes from static to dynamic and vice versa.

scholarly journals Dynamic Response Optimization of Complex Multibody Systems in a Penalty Formulation Using Adjoint Sensitivity

2015 ◽  
Vol 10 (3) ◽  
Author(s):  
Yitao Zhu ◽  
Daniel Dopico ◽  
Corina Sandu ◽  
Adrian Sandu
Keyword(s):  
Sensitivity Analysis ◽  
Multibody Dynamics ◽  
Multibody Systems ◽  
Real Life ◽  
Design Parameters ◽  
Vehicle Model ◽  
Adjoint Sensitivity ◽  
Penalty Formulation ◽  
Sensitivity Approach ◽  
Dynamic Performance Analysis

Multibody dynamics simulations are currently widely accepted as valuable means for dynamic performance analysis of mechanical systems. The evolution of theoretical and computational aspects of the multibody dynamics discipline makes it conducive these days for other types of applications, in addition to pure simulations. One very important such application is design optimization for multibody systems. In this paper, we focus on gradient-based optimization in order to find local minima. Gradients are calculated efficiently via adjoint sensitivity analysis techniques. Current approaches have limitations in terms of efficiently performing sensitivity analysis for complex systems with respect to multiple design parameters. To improve the state of the art, the adjoint sensitivity approach of multibody systems in the context of the penalty formulation is developed in this study. The new theory developed is then demonstrated on one academic case study, a five-bar mechanism, and on one real-life system, a 14 degree of freedom (DOF) vehicle model. The five-bar mechanism is used to validate the sensitivity approach derived in this paper. The full vehicle model is used to demonstrate the capability of the new approach developed to perform sensitivity analysis and optimization for large and complex multibody systems with respect to multiple design parameters with high efficiency.

scholarly journals Optimization of the cross-sectional shape of the belts of trihedral lattice supports

2019 ◽  
Vol 7 (4) ◽  
pp. 5-8
Author(s):  
Linar Sabitov ◽  
Ilnar Baderddinov ◽  
Anton Chepurnenko
Keyword(s):  
Objective Function ◽  
Nonlinear Optimization ◽  
Cross Section ◽  
Optimization Methods ◽  
Cross Sectional ◽  
Maximum Value ◽  
Axial Moment ◽  
The Cross ◽  
Nonlinear Optimization Methods ◽  
Sectional Shape

The article considers the problem of optimizing the geometric parameters of the cross section of the belts of a trihedral lattice support in the shape of a pentagon. The axial moment of inertia is taken as the objective function. Relations are found between the dimensions of the pentagonal cross section at which the objective function takes the maximum value. We introduce restrictions on the constancy of the consumption of material, as well as the condition of equal stability. The solution is performed using nonlinear optimization methods in the Matlab environment.

Nonlinear Schrodinger Equation-Based Adjoint Sensitivity Analysis

2021 ◽  
Vol 35 (11) ◽  
pp. 1342-1343
Author(s):  
Mahmoud Maghrabi ◽  
Mohamed Bakr ◽  
Shiva Kumar
Keyword(s):  
Sensitivity Analysis ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Adjoint System ◽  
Nonlinear Schrodinger Equation ◽  
Design Parameters ◽  
Adjoint Sensitivity Analysis ◽  
Adjoint Sensitivity ◽  
Nonlinear Schrödinger

A general nonlinear adjoint sensitivity analysis (ASA) approach for the time-dependent nonlinear Schrodinger equation (NLSE) is presented. The proposed algorithm estimates the sensitivities of a desired objective function with respect to all design parameters using only one extra adjoint system simulation. The approach efficiency is shown here through a numerical example.

Derivatives and Parameter Designs of Arbitrary Cross-Section Inhomogenous Beams’ Modes

2013 ◽  
Author(s):  
J. W. Xing ◽  
G. T. Zheng
Keyword(s):  
Cantilever Beam ◽  
Cross Section ◽  
Analytical Solutions ◽  
Structural Parameters ◽  
Arbitrary Cross Section ◽  
Mode Shapes ◽  
Design Parameters ◽  
Structural Parameter ◽  
Highly Sensitive ◽  
Sensitivity Analysis Method

As highly sensitive to structural parameter variations, it is necessary to study relations between derivatives of displacement modes and structural design parameters. This paper proposes an integral technique for obtaining the analytical solutions of slope and curvature modes of arbitrary cross-section inhomogeneous cantilever beam. The method is validated by comparing the computation results of modal frequencies and shapes with both numerical and analytical solutions. Furthermore, based on the presented method, we have established explicit expressions for the structural parameters sensitivity of the slope/curvature mode shapes. An example of parameter design is also presented for a cantilever beam with the proposed sensitivity analysis method.

scholarly journals Sensitivity analysis of free torsional vibration frequencies of thin-walled laminated beams under axial load

2019 ◽  
Vol 32 (5) ◽  
pp. 1347-1356 ◽  
Author(s):  
Czesław Szymczak ◽  
Marcin Kujawa
Keyword(s):  
Sensitivity Analysis ◽  
Cross Section ◽  
Torsional Vibration ◽  
Volume Fraction ◽  
Fibre Volume Fraction ◽  
Vibration Frequencies ◽  
Cross Sectional ◽  
First Order ◽  
Thin Walled ◽  
Frequency Changes

AbstractThe paper addresses sensitivity analysis of free torsional vibration frequencies of thin-walled beams of bisymmetric open cross section made of unidirectional fibre-reinforced laminate. The warping effect and the axial end load are taken into account. The consideration is based upon the classical theory of thin-walled beams of non-deformable cross section. The first-order sensitivity variation of the frequencies is derived with respect to the design variable variations. The beam cross-sectional dimensions and the material properties are assumed the design variables undergoing variations. The paper includes a numerical example related to simply supported I-beams and the distributions of sensitivity functions of frequencies along the beam axis. Accuracy is discussed of the first-order sensitivity analysis in the assessment of frequency changes due to the fibre volume fraction variable variations, and the effect of axial loads is discussed too.

Design of composite helicopter rotor blades to meet given cross-sectional properties

2005 ◽  
Vol 109 (1100) ◽  
pp. 471-475 ◽  
Author(s):  
S. L. Lemanski ◽  
P. M. Weaver ◽  
G. F. J. Hill
Keyword(s):  
Finite Element ◽  
Objective Function ◽  
Helicopter Rotor ◽  
Design Parameters ◽  
Stochastic Methods ◽  
Element Analysis ◽  
Cross Sectional ◽  
Design Variables ◽  
Non Linear ◽  
Optimisation Methods

Abstract This paper examines the design of a composite helicopter rotor blade to meet given cross-sectional properties. As with many real-world problems, the choice of objective and design variables can lead to a problem with a non-linear and/or non-convex objective function, which would require the use of stochastic optimisation methods to find an optimum. Since the objective function is evaluated from the results of a finite element analysis of the cross section, the computational expense of using stochastic methods would be prohibitive. It is shown that by choosing appropriate simplified design variables, the problem becomes convex with respect to those design variables. This allows deterministic optimisation methods to be used, which is considerably more computationally efficient than stochastic methods. It is also shown that the design variables can be chosen such that the response of each individual cross-sectional property can be closely modelled by a linear approximation, even though the response of a single objective function to many design parameters is non-linear. The design problem may therefore be reformulated into a number of simultaneous linear equations that are easily solved by matrix methods, thus allowing an optimum to be located with the minimum number of computationally expensive finite element analyses.

scholarly journals Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: V. Computation of Mixed 2nd-Order Sensitivities Involving Isotopic Number Densities

Energies ◽  
2020 ◽  
Vol 13 (10) ◽  
pp. 2580 ◽  
Author(s):  
Ruixian Fang ◽  
Dan G. Cacuci
Keyword(s):  
Sensitivity Analysis ◽  
Cross Section ◽  
Cross Sections ◽  
Second Order ◽  
Adjoint Sensitivity Analysis ◽  
Number Density ◽  
Reactor Physics ◽  
Adjoint Sensitivity ◽  
Energy Group ◽  
Analysis Methodology

This work applies the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) to compute the mixed 2nd-order sensitivities of a polyethylene-reflected plutonium (PERP) benchmark’s leakage response with respect to the benchmark’s imprecisely known isotopic number densities and the other benchmark imprecisely known parameters, including: (i) the 6 × 180 mixed 2nd-order sensitivities involving the total microscopic cross sections; (ii) the 6 × 21,600 mixed 2nd-order sensitivities involving the scattering microscopic cross sections; (iii) the 6 × 60 mixed 2nd-order sensitivities involving the fission microscopic cross sections; and (iv) the 6 × 60 mixed 2nd-order sensitivities involving the average number of neutrons produced per fission. It is shown that many of these mixed 2nd-order sensitivities involving the isotopic number densities have very large values. Most of the large sensitivities involve the isotopic number density of 239Pu, and the microscopic total, scattering or fission cross sections for the 12th or 30th energy groups of 239Pu or 1H, respectively. The 2nd-order mixed sensitivity of the PERP leakage response with respect to the isotopic number density of 239Pu and the microscopic total cross section for the 30th energy group of 1H is the largest of the above mentioned sensitivities, attaining the value −94.91.

Failure Analysis of a Qualification Unit Injector for a Satellite Thruster

1998 ◽  
Author(s):  
M. Lipschutz ◽  
R. Brannam ◽  
T. Nguyentat
Keyword(s):  
Failure Analysis ◽  
Cross Section ◽  
Combustion Products ◽  
Design Parameters ◽  
Cross Sectional ◽  
X Ray ◽  
Root Cause ◽  
Qualification Testing ◽  
Non Destructive ◽  
Unit Injector

Abstract This article details the results of a failure analysis performed on a Qualification Unit injector for a military satellite thrusters and explains that the failure was initially detected due to a shift in performance during qualification testing. Failure analysis involved non-destructive evaluation on the injector using micro-focus X-ray and scanning electron microscopy. Serial cross-sectional metallography was then performed, with each cross-section documented by optical microscopy and SEM. The failure analysis resulted in three main conclusions: (1) the root cause of the failure was attributed to multiple detonations in or around the damaged orifice; these detonations were likely caused by fuel and/or combustion products condensing in the orifice between pulses and then igniting during a subsequent pulse; (2) multiple damage mechanisms were identified in addition to the ZOT detonations; and (3) the material and platelet manufacturing process met all design parameters.

A Novel Theoretical Approach to Passive Control of Thermo-Acoustic Oscillations: Application to Ducted Heat Sources

2013 ◽  
Author(s):  
Luca Magri ◽  
Matthew P. Juniper
Keyword(s):  
Heat Release ◽  
Passive Control ◽  
Adjoint Equations ◽  
Heat Sources ◽  
Acoustic System ◽  
Acoustic Oscillations ◽  
Hot Wire ◽  
Adjoint Sensitivity ◽  
Cross Sectional ◽  
Rijke Tube

In this paper, we develop a linear technique that predicts how the stability of a thermo-acoustic system changes due to the action of a generic passive feedback device or a generic change in the base state. From this, one can calculate the passive device or base state change that most stabilizes the system. This theoretical framework, based on adjoint equations, is applied to two types of Rijke tube. The first contains an electrically-heated hot wire and the second contains a diffusion flame. Both heat sources are assumed to be compact so that the acoustic and heat release models can be decoupled. We find that the most effective passive control device is an adiabatic mesh placed at the downstream end of the Rijke tube. We also investigate the effects of a second hot wire and a local variation of the cross-sectional area but find that both affect the frequency more than the growth rate. This application of adjoint sensitivity analysis opens up new possibilities for the passive control of thermo-acoustic oscillations. For example, the influence of base state changes can be combined with other constraints, such as that the total heat release rate remains constant, in order to show how an unstable thermo-acoustic system should be changed in order to make it stable.

Sign in / Sign up

Export Citation Format

Share Document