3 The contribution of individual element stiffnesses to the overall structural stiffness matrix

1994 ◽  
pp. 29-32
Keyword(s):  
Stiffness Matrix ◽  
Individual Element ◽  
Structural Stiffness

Derivation of New Transcendental Member Stiffness Determinant for Vibrating Frames

2003 ◽  
Vol 03 (02) ◽  
pp. 299-305 ◽  
Author(s):  
F. W. Williams ◽  
D. Kennedy
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stiffness Matrix ◽  
Infinite Order ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Structural Stiffness ◽  
Trial And Error ◽  
Stiffness Matrices ◽  
Vibration Problems

Transcendental dynamic member stiffness matrices for vibration problems arise from solving the governing differential equations to avoid the conventional finite element method (FEM) discretization errors. Assembling them into the overall dynamic structural stiffness matrix gives a transcendental eigenproblem, whose eigenvalues (natural frequencies or their squares) are found with certainty using the Wittrick–Williams algorithm. This paper gives equations for the recently discovered transcendental member stiffness determinant, which equals the appropriately normalized FEM dynamic stiffness matrix determinant of a clamped ended member modelled by infinitely many elements. Multiplying the overall transcendental stiffness matrix determinant by the member stiffness determinants removes its poles to improve curve following eigensolution methods. The present paper gives the first ever derivation of the Bernoulli–Euler member stiffness determinant, which was previously found by trial-and-error and then verified. The derivation uses the total equivalence of the transcendental formulation and an infinite order FEM formulation, which incidentally gives insights into conventional FEM results.

Static and Dynamic Analysis of Multi-Story Buildings, Including P-Delta Effects

1987 ◽  
Vol 3 (2) ◽  
pp. 289-298 ◽  
Author(s):  
E. L. Wilson ◽  
A. Habibullah
Keyword(s):  
Dynamic Analysis ◽  
Stiffness Matrix ◽  
Mode Shapes ◽  
Building Structures ◽  
Structural Stiffness ◽  
Lateral Loads ◽  
Static And Dynamic Analysis ◽  
Geometric Stiffness ◽  
Area Of Concern ◽  
Structural Engineers

The P-Delta phenomenon is an area of concern to structural engineers. Traditional methods for incorporating P-Delta effects in analysis are based on iterative techniques. These techniques are time-consuming and are in general used for static analysis only. For building structures, the mass, which causes the P-Delta effect, is constant irrespective of the lateral loads and displacements. This information is used to linearize the P-Delta effect for buildings and solve the problem “exactly”, satisfying equilibrium in the deformed position, without iterations. An algorithm is developed that incorporates the P-Delta effects into the basic formulation of the structural stiffness matrix as a geometric stiffness correction. This procedure can be used for both static and dynamic analysis and will account for the lengthening of the structural time periods and changes in mode shapes due to P-Delta effects. The algorithm can be directly incorporated into building analysis programs.

scholarly journals Experimental Studies on Damage Detection in Frame Structures Using Vibration Measurements

2010 ◽  
Vol 17 (6) ◽  
pp. 697-721 ◽  
Author(s):  
Giancarlo Fraraccio ◽  
Adrian Brügger ◽  
Raimondo Betti
Keyword(s):  
Time Domain ◽  
Stiffness Matrix ◽  
Structural Damage ◽  
Experimental Testing ◽  
Experimental Studies ◽  
Frame Structures ◽  
Identification Algorithm ◽  
Structural Stiffness ◽  
Domain Identification ◽  
Frequency Domain Decomposition

This paper presents an experimental study of frequency and time domain identification algorithms and discusses their effectiveness in structural health monitoring of frame structures using acceleration input and response data. Three algorithms were considered: 1) a frequency domain decomposition algorithm (FDD), 2) a time domain Observer Kalman IDentification algorithm (OKID), and 3) a subsequent physical parameter identification algorithm (MLK). Through experimental testing of a four-story steel frame model on a uniaxial shake table, the inherent complications of physical instrumentation and testing are explored. Primarily, this study aims to provide a dependable first-order and second-order identification of said test structure in a fully instrumented state. Once the characteristics (i.e. the stiffness matrix) for a benchmark structure have been determined, structural damage can be detected by a change in the identified structural stiffness matrix. This work also analyzes the stability of the identified structural stiffness matrix with respect to fluctuations of input excitation magnitude and frequency content in an experimental setting.

X-ray microtomography

1988 ◽  
Vol 46 ◽  
pp. 998-999
Author(s):  
H.W. Deckman ◽  
B.F. Flannery ◽  
J.H. Dunsmuir ◽  
K.D' Amico
Keyword(s):  
Computed Tomography ◽  
Internal Structure ◽  
Imaging Technique ◽  
Three Dimensional ◽  
Tissue Structure ◽  
Individual Element ◽  
X Ray ◽  
Non Invasive ◽  
Panoramic Imaging ◽  
Three Dimensional Images

We have developed a new X-ray microscope which produces complete three dimensional images of samples. The microscope operates by performing X-ray tomography with unprecedented resolution. Tomography is a non-invasive imaging technique that creates maps of the internal structure of samples from measurement of the attenuation of penetrating radiation. As conventionally practiced in medical Computed Tomography (CT), radiologists produce maps of bone and tissue structure in several planar sections that reveal features with 1mm resolution and 1% contrast. Microtomography extends the capability of CT in several ways. First, the resolution which approaches one micron, is one thousand times higher than that of the medical CT. Second, our approach acquires and analyses the data in a panoramic imaging format that directly produces three-dimensional maps in a series of contiguous stacked planes. Typical maps available today consist of three hundred planar sections each containing 512x512 pixels. Finally, and perhaps of most import scientifically, microtomography using a synchrotron X-ray source, allows us to generate maps of individual element.

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