Non-Linear Sensitivity Analysis of Mechanical Structures Using Modal Data

1991 ◽  
Vol 205 (1) ◽  
pp. 67-75 ◽  
Author(s):  
W M To ◽  
D J Ewins
Keyword(s):  
Sensitivity Analysis ◽  
Measurement Errors ◽  
Structural Modification ◽  
Element Model ◽  
Rayleigh Quotient ◽  
Second Order ◽  
Frame Structure ◽  
Original Structure ◽  
Modal Properties ◽  
Non Linear

This paper presents a new procedure for determining the revised modal properties (eigenvalues and mass-normalized eigenvectors) in a structural modification analysis. The procedure is based on expressing the eigenvectors of the modified structure as a linear combination of the eigenvectors of the original structure and employs the stationary property of the Rayleigh quotient to determine the modified structure's eigenvalues. It has the same theoretical basis as first- and second-order sensitivity analysis, but here the non-linear effects contributed by all high-order terms [generally assumed to be small relative to the effect contributed by first- and second-order terms (1–6)] are preserved in full. Hence, the usual shortcoming of sensitivity analysis—that it is limited to small modifications—is overcome. A special feature of this procedure is that the exact modal properties of the modified structure are determined without solving the generalized eigenvalue problem for the modified structure. Thus, this procedure can greatly reduce the computation cost and increase the efficiency of structural modification analysis (or reanalysis) during a structural optimization process. Numerical examples demonstrate the superconvergence characteristic of the technique. The limitations caused by modal and coordinate incompleteness, and the sensitivity of this technique with respect to simulated measurement errors, are investigated by using a finite element model of a steel frame structure and a ten-degrees-of-freedom mass-spring model.

First and Second Order Elastoplastic Analyses of Thin-Walled Metal Members using Generalized Beam Theory

2018 ◽  
Author(s):  
Miguel Abambres
Keyword(s):  
Finite Element ◽  
Stainless Steel ◽  
Cross Section ◽  
Beam Theory ◽  
Second Order ◽  
Flow Rule ◽  
Non Linear ◽  
Thin Walled ◽  
Shell Finite Element ◽  
Generalized Beam Theory

Original Generalized Beam Theory (GBT) formulations for elastoplastic first and second order (postbuckling) analyses of thin-walled members are proposed, based on the J2 theory with associated flow rule, and valid for (i) arbitrary residual stress and geometric imperfection distributions, (ii) non-linear isotropic materials (e.g., carbon/stainless steel), and (iii) arbitrary deformation patterns (e.g., global, local, distortional, shear). The cross-section analysis is based on the formulation by Silva (2013), but adopts five types of nodal degrees of freedom (d.o.f.) – one of them (warping rotation) is an innovation of present work and allows the use of cubic polynomials (instead of linear functions) to approximate the warping profiles in each sub-plate. The formulations are validated by presenting various illustrative examples involving beams and columns characterized by several cross-section types (open, closed, (un) branched), materials (bi-linear or non-linear – e.g., stainless steel) and boundary conditions. The GBT results (equilibrium paths, stress/displacement distributions and collapse mechanisms) are validated by comparison with those obtained from shell finite element analyses. It is observed that the results are globally very similar with only 9% and 21% (1st and 2nd order) of the d.o.f. numbers required by the shell finite element models. Moreover, the GBT unique modal nature is highlighted by means of modal participation diagrams and amplitude functions, as well as analyses based on different deformation mode sets, providing an in-depth insight on the member behavioural mechanics in both elastic and inelastic regimes.

scholarly journals Evaluation of Moisture and Decay Models for a New Design Framework for Decay Prediction of Wood

Forests ◽  
2021 ◽  
Vol 12 (6) ◽  
pp. 721
Author(s):  
Jonas Niklewski ◽  
Philip Bester van Niekerk ◽  
Christian Brischke ◽  
Eva Frühwald Hansson
Keyword(s):  
Service Life ◽  
Wood Decay ◽  
Element Model ◽  
Digital Design ◽  
Design Guideline ◽  
Digital Performance ◽  
Detail Design ◽  
Non Linear ◽  
Service Life Design ◽  
Life Design

Performance-based, service-life design of wood has been the focus of much research in recent decades. Previous works have been synthesized in various factorized design frameworks presented in the form of technical reports. Factorization does not consider the non-linear dependency between decay-influencing effects, such as between detail design and climate variables. The CLICKdesign project is a joint European effort targeting digital, performance-based specification for service-life design (SLD) of wood. This study evaluates the feasibility of using a semi-empirical moisture model (SMM) as a basis for a digital SLD framework. The performance of the SMM is assessed by comparison against a finite element model (FEM). In addition, two different wood decay models (a logistic, LM, and simplified logistic model (SLM)) are compared. While discrepancies between the SMM and FEM were detected particularly at high wood moisture content, the overall performance of the SMM was deemed sufficient for the application. The main source of uncertainty instead stems from the choice of wood decay model. Based on the results, a new method based on pre-calculated time series, empirical equations, and interpolation is proposed for predicting the service life of wood. The method is fast and simple yet able to deal with non-linear effects between weather variables and the design of details. As such, it can easily be implemented as part of a digital design guideline to provide decision support for architects and engineers, with less uncertainty than existing factorized guidelines.

scholarly journals Non-Linear Neutral Differential Equations with Damping: Oscillation of Solutions

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 285
Author(s):  
Saad Althobati ◽  
Jehad Alzabut ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Oscillatory Behavior ◽  
Order Equation ◽  
Second Order ◽  
Riccati Technique ◽  
Neutral Equations ◽  
Neutral Differential Equations ◽  
Main Equation ◽  
Non Linear ◽  
Even Order

The oscillation of non-linear neutral equations contributes to many applications, such as torsional oscillations, which have been observed during earthquakes. These oscillations are generally caused by the asymmetry of the structures. The objective of this work is to establish new oscillation criteria for a class of nonlinear even-order differential equations with damping. We employ different approach based on using Riccati technique to reduce the main equation into a second order equation and then comparing with a second order equation whose oscillatory behavior is known. The new conditions complement several results in the literature. Furthermore, examining the validity of the proposed criteria has been demonstrated via particular examples.

Stochastic Sensitivity Analysis of Structural Systems With Interval Uncertainties

2013 ◽  
Author(s):  
Giuseppe Muscolino ◽  
Roberta Santoro ◽  
Alba Sofi
Keyword(s):  
Sensitivity Analysis ◽  
Series Expansion ◽  
Neumann Series ◽  
Mean Value ◽  
Frame Structure ◽  
Young’S Moduli ◽  
Rational Series ◽  
Power Spectral ◽  
Stochastic Sensitivity Analysis ◽  
Neumann Series Expansion

Interval sensitivity analysis of linear discretized structures with uncertain-but-bounded parameters subjected to stationary multi-correlated Gaussian stochastic processes is addressed. The proposed procedure relies on the use of the so-called Interval Rational Series Expansion (IRSE), recently proposed by the authors as an alternative explicit expression of the Neumann series expansion for the inverse of a matrix with a small rank-r modification and properly extended to handle also interval matrices. The IRSE allows to derive approximate explicit expressions of the interval sensitivities of the mean-value vector and Power Spectral Density (PSD) function matrix of the interval stationary stochastic response. The effectiveness of the proposed method is demonstrated through numerical results pertaining to a seismically excited three-storey frame structure with interval Young’s moduli of some columns.

scholarly journals Perturbations of nonlinear autonomous oscillators

1994 ◽  
Vol 35 (4) ◽  
pp. 445-468 ◽  
Author(s):  
P. B. Chapman
Keyword(s):  
General Theory ◽  
Fourier Coefficients ◽  
Multiple Scales ◽  
Second Order ◽  
Multiple Scales Method ◽  
Suitable Parameter ◽  
Non Linear

AbstractA general theory is given for autonomous perturbations of non-linear autonomous second order oscillators. It is found using a multiple scales method. A central part of it requires computation of Fourier coefficients for representation of the underlying oscillations, and these coefficients are found as convergent expansions in a suitable parameter.

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