Date of Award

Fall 1994

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Civil Engineering - (Ph.D.)

Department

Civil and Environmental Engineering

First Advisor

C.T. Thomas Hsu

Second Advisor

William R. Spillers

Third Advisor

M. Ala Saadeghvaziri

Fourth Advisor

Edward G. Dauenheimer

Fifth Advisor

Rong-Yaw Chen

Abstract

Applying spline functions to numerical structural analysis has been more common in recent years. The recent increase use of spline functions is mainly due to their excellent characteristics, such as sectionalized continuity, linear combination, flexibility, and easy use for various boundary conditions. The whole deformed shape of some structures or substructures can be described with one displacement function constructed by a series of spline functions. By doing this, the mesh generation and the huge computer memory space are no longer needed because only one single superelement can be used in the whole process. The choice of spline functions as displacement functions has many advantages that have been demonstrated by several researchers for a limited range of structures. More extensive research on using spline functions in structural analysis hereafter can be expected. This research work represents an effort in that direction.

Based on cubic B-spline functions, this dissertation presents static and free vibration analysis of arbitrary quadrilateral flexural plates with various boundary conditions. Combination of cubic B-spline functions in two orthogonal directions constructs a superelement for the whole plate. The cubic B-spline displacement function has been formed to efficiently model the deflection shape and to yield more accurate results. A further step has been taken in the present research to apply the cubic B-spline function to a nonlinear problem. A numerical method is developed for the determination of complete load-deflection and moment-curvature relationships for slender reinforced concrete columns with arbitrary cross sections under combined biaxial flexure and axial load. Improvement of computer time and accuracy has been demonstrated obviously due to the application of cubic B-spline function and introduction of p-multiplier in the numerical formulation.

Comparison of present analysis with analytical solutions, other numerical methods, and experimental results, appears to have a good agreement.

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