scholarly journals Maximum Displacement Variability of Stochastic Structures Subject to Deterministic Earthquake Loading

1998 ◽  
Vol 5 (5-6) ◽  
pp. 355-369
Author(s):  
L.L. Graham
Keyword(s):  
Material Properties ◽  
Mass Density ◽  
Upper Bounds ◽  
Maximum Response ◽  
Frame Structures ◽  
Earthquake Loading ◽  
Response Functions ◽  
Maximum Displacement ◽  
Function Formulation ◽  
Variability Response Function

The variability of the maximum response displacement of random frame structures under deterministic earthquake loading are examined in this paper using stochastic finite element techniques. The elastic modulus and the mass density are assumed to be described by cross-correlated stochastic fields. Specifically, a variability response function formulation is used for this problem, which allows for calculation of spectral-distribution-free upper bounds of the maximum displacement variance. Further, under the assumption of prespecified correlation functions describing the spatial variation of the material properties, variability response functions are used to calculate the corresponding maximum displacement variance. Two numerical examples are provided to demonstrate the methodology. Results show that randomness in the material properties can lead to significant uncertainty in the maximum response displacement.

Design Forces for Drift and Damage Control: A Second Look at the Substitute Structure Approach

1994 ◽  
Vol 10 (2) ◽  
pp. 319-331 ◽  
Author(s):  
John F. Bonacci
Keyword(s):  
Reinforced Concrete ◽  
Damage Control ◽  
Dynamic Test ◽  
Frame Structures ◽  
Rc Frame ◽  
Test Results ◽  
Structure Approach ◽  
Maximum Displacement ◽  
Design Loads ◽  
Rc Frame Structures

This paper explores the development of a method that is useful for design of reinforced concrete (RC) frame structures to resist earthquakes. The substitute structure method, originally proposed in the 1970s, makes an analogy between viscously damped linear and hysteretic response for the purpose of estimating maximum displacement. The evolution of the method is retraced in order to emphasize its unique reliance on experimental results, which are needed to establish rules for assignment of substitute linear properties. Recent dynamic test results are used to extend significantly the calibration of the method, which furnishes design loads on the basis of drift and damage control.

Probabilistic Oblique Impact Analysis of Functionally Graded Plates – A Multivariate Adaptive Regression Splines Approach

2021 ◽  
Author(s):  
P. K. Karsh ◽  
Bindi Thakkar ◽  
R. R. Kumar ◽  
Vaishali ◽  
Sudip Dey
Keyword(s):  
Material Properties ◽  
Mass Density ◽  
Plate Thickness ◽  
Functionally Graded ◽  
Multivariate Adaptive Regression Splines ◽  
Low Velocity Impact ◽  
Fe Model ◽  
Low Velocity ◽  
Velocity Impact ◽  
Mars Model

Purpose: To investigate the probabilistic low-velocity impact of functionally graded (FG) plate using the MARS model, considering uncertain system parameters. Design/methodology/application: The distribution of various material properties throughout FG plate thickness is calculated using power law. For finite element (FE) formulation, isoparametric elements with eight nodes are considered, each component has five degrees of freedom. The combined effect of variability in material properties such as elastic modulus, modulus of rigidity, Poisson’s ratio, and mass density are considered. The surrogate model is validated with the FE model represented by the scatter plot and the probability density function (PDF) plot based on Monte Carlo simulation (MCS). Findings: The outcome of the degree of stochasticity, impact angle, impactor’s velocity, impactor’s mass density, and point of impact on the maximum value of contact force (CFmax ), plate deformation (PDmax), and impactor deformation (IDmax ) are determined. A convergence study is also performed to determine the optimal number of the constructed MARS model’s sample size. Originality/value: The results illustrate the significant effects of uncertain input parameters on FGM plates’ low-velocity impact responses by employing a surrogate-based MARS model.

scholarly journals Free vibration of frame structures made of Zener type viscoelastic material

2019 ◽  
Vol 285 ◽  
pp. 00009
Author(s):  
Roman Lewandowski ◽  
Przemysław Wielentejczyk
Keyword(s):  
Rheological Properties ◽  
Viscoelastic Material ◽  
Dynamic Characteristics ◽  
Frame Structures ◽  
Response Functions ◽  
Zener Model ◽  
Linear Eigenvalue Problem ◽  
Viscoelastic Structure ◽  
Properties Of Materials ◽  
Fractional Zener Model

A method for determining the dynamic characteristics of structures made of viscoelastic material is presented. The fractional Zener model is used to the describe the rheological properties of materials. All of the elements of a structure must be built of material with identical rheological properties. The solution to the linear eigenvalue problem for some elastic structure and the solution to a single nonlinear algebraic equation are needed to obtain the dynamic characteristics of a viscoelastic structure. Moreover, the frequency response functions are determined in a very efficient way. The results of a representative calculation are presented and briefly discussed.

On a class of non-dissipative materials that are not hyperelastic

2008 ◽  
Vol 465 (2102) ◽  
pp. 493-500 ◽  
Author(s):  
K.R Rajagopal ◽  
A.R Srinivasa
Keyword(s):  
Physical Meaning ◽  
Constitutive Equations ◽  
Mechanical Response ◽  
Mass Density ◽  
Cauchy Stress ◽  
Response Functions ◽  
State Variables ◽  
Hyperelastic Materials ◽  
Current Mass ◽  
Helmholtz Potential

The purpose of this brief note is to develop fully Eulerian, implicit constitutive equations for the mechanical response of a class of materials that do not dissipate mechanical work in any process. We show that such materials can be modelled by obtaining a form for the Helmholtz potential as a function of the current mass density, the Cauchy stress and certain other parameters that capture anisotropic response. The resulting constitutive equations are of the form , where and are functions of the state variables of the system. The class of materials that can be obtained from such a constitutive relation is considerably more general than conventional Green-elastic hyperelastic materials. Such response functions may be suitable for the modelling of biological tissue where, due to the constant remodelling that takes place, there may be no physical meaning to a ‘reference configuration’.

Model updating–based damage detection of a concrete beam utilizing experimental damped frequency response functions

2018 ◽  
Vol 22 (4) ◽  
pp. 935-947 ◽  
Author(s):  
Qianhui Pu ◽  
Yu Hong ◽  
Liangjun Chen ◽  
Shili Yang ◽  
Xikun Xu
Keyword(s):  
Damage Detection ◽  
Frequency Response ◽  
Frequency Response Function ◽  
Concrete Beam ◽  
Model Updating ◽  
Response Functions ◽  
Experimental Frequency ◽  
Frequency Response Functions ◽  
Function Formulation ◽  
Analytical Frequency

This article evaluates the use of experimental frequency response functions for damage detection and quantification of a concrete beam with the help of model updating theory. The approach is formulated as an optimization problem that intends to adjust the analytical frequency response functions from a benchmark finite element model to match with the experimental frequency response functions from the damaged structure. Neither model expansion nor reduction is needed because the individual analytical frequency response function formulation is derived. Unlike the commonly used approaches that assume zero damping or viscous damping for simplicity, a more realistic hysteretic damping model is considered in the analytical frequency response function formulation. The accuracy and anti-noise ability of the proposed approach are first verified by the numerical simulations. Next, a laboratory reinforced concrete beam with different levels of damage is utilized to investigate the applicability in an actual test. The results show successful damage quantification and damping updating of the beam by matching the analytical frequency response functions with the experimental frequency response functions in each damage scenario.

Variability response functions for apparent material properties

2016 ◽  
Vol 44 ◽  
pp. 28-34 ◽  
Author(s):  
Sanjay R. Arwade ◽  
George Deodatis ◽  
Kirubel Teferra
Keyword(s):  
Material Properties ◽  
Response Functions

Dynamics of Viscoelastic Structures—A Time-Domain, Finite Element Formulation

1985 ◽  
Vol 52 (4) ◽  
pp. 897-906 ◽  
Author(s):  
D. F. Golla ◽  
P. C. Hughes
Keyword(s):  
Finite Element ◽  
Material Properties ◽  
Mass Density ◽  
Viscoelastic Damping ◽  
Element Formulation ◽  
Elastic Structures ◽  
Element Analysis ◽  
Modal Damping ◽  
Computer Based ◽  
Finite Element Formulations

Mathematical models of elastic structures have become very sophisticated: given the crucial material properties (mass density and the several elastic moduli), computer-based techniques can be used to construct exotic finite element models. By contrast, the modeling of damping is usually very primitive, often consisting of no more than mere guesses at “modal damping factors.” The aim of this paper is to raise the modeling of viscoelastic structures to a level consistent with the modeling of elastic structures. Appropriate material properties are identified which permit the standard finite element formulations used for undamped structures to be extended to viscoelastic structures. Through the use of “dissipation” coordinates, the canonical “M, K” form of the undamped motion equations is expanded to encompass viscoelastic damping. With this formulation finite element analysis can be used to model viscoelastic damping accurately.

scholarly journals Material Properties of Human Ocular Tissue at 7-µm Resolution

2017 ◽  
Vol 39 (5) ◽  
pp. 313-325 ◽  
Author(s):  
Daniel Rohrbach ◽  
Kazuyo Ito ◽  
Harriet O. Lloyd ◽  
Ronald H. Silverman ◽  
Kenji Yoshida ◽  
...  
Keyword(s):  
Light Microscopy ◽  
Material Properties ◽  
Quantitative Assessment ◽  
Mass Density ◽  
Acoustic Microscopy ◽  
Ocular Tissue ◽  
Acoustic Parameters ◽  
Ocular Tissues ◽  
Ultrasound Attenuation ◽  
Ophthalmic Diseases

Quantitative assessment of the material properties of ocular tissues can provide valuable information for investigating several ophthalmic diseases. Quantitative acoustic microscopy (QAM) offers a means of obtaining such information, but few QAM investigations have been conducted on human ocular tissue. We imaged the optic nerve (ON) and iridocorneal angle in 12-µm deparaffinized sections of the human eye using a custom-built acoustic microscope with a 250-MHz transducer (7-µm lateral resolution). The two-dimensional QAM maps of ultrasound attenuation (α), speed of sound ( c), acoustic impedance ( Z), bulk modulus ( K), and mass density (ρ) were generated. Scanned samples were then stained and imaged by light microscopy for comparison with QAM maps. The spatial resolution and contrast of scanning acoustic microscopy (SAM) maps were sufficient to resolve anatomic layers of the retina (Re); anatomic features in SAM maps corresponded to those seen by light microscopy. Significant variations of the acoustic parameters were found. For example, the sclera was 220 MPa stiffer than Re, choroid, and ON tissue. To the authors’ knowledge, this is the first systematic study to assess c, Z, K, ρ, and α of human ocular tissue at the high ultrasound frequencies used in this study.

Identification of material properties of composite plates using Fourier-generated frequency response functions

2017 ◽  
Vol 26 (2) ◽  
pp. 119-128 ◽  
Author(s):  
Jun Hui Tam ◽  
Zhi Chao Ong ◽  
Chun Lek Lau ◽  
Zubaidah Ismail ◽  
Bee Chin Ang ◽  
...  
Keyword(s):  
Frequency Response ◽  
Material Properties ◽  
Composite Plates ◽  
Response Functions ◽  
Frequency Response Functions
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