vaniella palmelah hedwiga
Algernon Alcala
A first main application of Stabil is the static analysis of 2D and 3D frame and truss structures. Figure 1 shows the results of an analysis of a portal frame: after the definition of nodes, elements, boundary conditions and loads, the structure's stiffness matrix is available in the Matlab environment. Dedicated postprocessing routines are available for plotting the deformed structure and the member force distribution, tailored to a structural analysis.
Stabil also allows to perform a dynamic structural analysis. Figure 2 shows the eigenmodes of a portal frame, which form the basis of modal superposition techniques in the time or frequency domain. Other examples of dynamic structural analysis in Stabil include response spectra analysis, solution in the frequency domain, and direct time integration.
Apart from the structural analysis of 2D and 3D frame and truss structures, various element types are available in Stabil, including plate, shell, solid, and plane elements. The open implementation of Stabil further allows to study and modify existing or add new element types, according to the user's needs.
This means that everyone is free to use Stabil and to redistribute it on a free basis. Stabil is not in the public domain; it is copyrighted and there are restrictions on its distribution. For example, you cannot integrate Stabil, in full or in parts, in any closed-source software you plan to distribute (commercially or not).
Stabil has been initiated in the frame of OOI Project 2006/20 "An interactive and adaptive application for the static and dynamic analysis of structures", funded by the KU Leuven Educational Policy Unit. The financial support is gratefully acknowledged.
Analysis of beam, 2D and 3D truss, 2D and 3D frame and plane strain structures using the matrix displacement method. Introduction to the finite element method of analysis by deriving the element stiffness matrices using Virtual Work. Beam and frame elements include shearing deformation and geometric stiffness effects. Computer implementation of analysis procedures using MATLAB and commercial structural analysis software. Modeling issues including convergence, symmetry and antisymmetry. Introduction to structural dynamics. Credit not given for both CE 425 and CE 525.
This is an introductory level course to analysis of statically determinate and indeterminate structures. Main objective of this course is to introduce the students the displacement and stiffness methods.
Upon succesful completion of this course, a student will be able to
1. Recognize the difference between force and displacement based structural analysis methods
2. Analyze 2D frame structures using slope-deflection equations
3. Analyze 2D frame structures using the moment distribution method
4. Analyze 2D as well as 3D truss and frames structures using the stiffness method
5. Implement the stiffness method in a programming language
6. Develop influence lines for statically determinate and indeterminate structures
The dynamic analysis of a truss system modelled by the finite element method in the frequency domain is studied. The truss system is modelled by 22 elements and has 44 degrees of freedom. The stiffness matrix and mass matrix of the truss system are obtained by using the finite element method. Differential equations of the truss system are obtained by using the obtained stiffness and mass matrix. By applying the Laplace transformation, the displacements of each node are calculated, and the equation is arranged in the frequency domain. The obtained differential equations are solved by using MATLAB. Eigen values are calculated and represented depending on the frequencies. Thus, static displacements, dynamic displacements, static reaction forces and dynamic reaction forces for each frequency are graphically obtained. Additionally, dynamic amplification factors are calculated and simulated depending on the frequencies. Dynamic displacements increased near the eigenvalues, and the dynamic amplification factors also increased dramatically depending on the related eigenvalues. By avoiding the natural frequency, it is possible to design a better structure to reduce vibration.
c01484d022