M. Asghar Bhatti

A simple strain energy based finite element mesh refinement scheme

Abstract A simple technique for finite element mesh refinement is presented. The technique is based on maximizing strain energy in the elements. The implementation of the technique in a general purpose program is facilitated by the fact that all calculations can be made at the element level. An element-by-element iterative algorithm combining Jacobi and Gauss-Seidel iteration is presented for the solution of equilibrium equations. The algorithm does not require formulation of the global stiffness matrix. Several numerical examples from two-dimensional elasticity are presented to show the effectiveness of the algorithms developed.

A Non-Linear Fatigue Damage Model for Concrete in Tension

Although concrete is used primarily because of its properties under compressive loading, a knowledge of its tensile behavior is essential in situations in which cracking, and the resulting change in stiffness, are critical for the service and ultimate load behavior of a structure. One important aspect of the tensile behavior of concrete is its performance under cyclic loading. The majority of past studies on the tensile fatigue performance of concrete have focused on the behavior under constant amplitude loads. However, in recent years, the effect of variable amplitude loading has also been emphasized. In this paper a model is presented for fatigue damage accumulation for concrete subjected to nonconstant tensile cyclic loads. The model is based on the concepts of Continuum Damage Mechanics and is able to account for the nonlinear propagation and accumulation of fatigue damage. Calibration of the model is done using existing experimental data, and its validity is checked against recently published tests.

Investigation of Bonding Condition in Concrete Overlay by Laboratory Testing, Finite Element Modeling, and Field Evaluation

To evaluate the effect of bonded versus unbonded condition in concrete overlay structure, a field evaluation, laboratory experiment, and 3-D finite element analysis (FEA) model were carried out. First, a field evaluation of bonded and unbonded pavement test sections in Iowa was performed. Cores were extracted from existing pavements and tested for their bond strengths with shear testing equipment. The bond strength between an overlay and the existing pavement gradually increased over time, regardless of the initial bond strength. In some cases, an insufficient bond shear strength at the interface between the concrete overlay and the existing pavement seemed to have contributed to increased distress on the overlay surface. Second, a laboratory experiment was conducted to investigate an effect of bonding in pavement structure. Concrete cylinder specimens that were one-half regular concrete and one-half polymer concrete were fabricated, and their indirect tensile strength was measured at the bonding interfac...

PRELIMINARY OPTIMAL DESIGN OF CABLE-STAYED BRIDGES

A methodology for preliminary design of cable-stayed bridges using optimization techniques is presented. A simple model of the bridge, comprising beam elements for the longitudinal deck girder and lower and truss elements for stay cables, is used. The computer program SADDLE is used for optimization. Constraints are placed on stresses, displacements and member sizes under multiple loading conditions. The methodology enables the designer to vary the arrangement and size of stay cables and cross-sectional dimensions of the longitudinal deck girder. Consequently an aesthetically pleasing as well as an economical and feasible design of a cable-stayed bridge can be obtained quickly and efficiently.

Parametric modeling of earthquake response spectra

Abstract A mathematical model for the response spectra is determined using statistical analysis. The form of the model is first established using fifty computer simulated accelerograms. The final form is then used on twenty-five accelerograms from fifteen past United States earthquakes. This model smooths out peaks and valleys which are characteristic of the response spectrum of any single earthquake. Thus it serves as a ‘smooth design spectrum’ and can be used to approximate structural response to a future seismic event.

Interior Point Methods

The simplex method starts from a basic feasible solution and moves along the boundary of the feasible region until an optimum is reached. At each step, the algorithm brings only one new variable into the basic set, regardless of the total number of variables. Thus, for problems with a large number of variables, the method may take many steps before terminating. In fact, relatively simple examples exist in which the simplex method visits all vertices of the feasible region before finding the optimum.

Optimization Problem Formulation

Optimization problems arise naturally in many different disciplines. A structural engineer designing a multistory building must choose materials and proportions for different structural components in the building in order to have a safe structure that is as economical as possible. A portfolio manager for a large mutual fund company must choose investments that generate the largest possible rate of return for its investors while keeping the risk of major losses to acceptably low levels. A plant manager in a manufacturing facility must schedule the plant operations such that the plant produces products that maximize company’s revenues while meeting customer demands for different products and staying within the available resource limitations. A scientist in a research laboratory may be interested in finding a mathematical function that best describes an observed physical phenomenon.

Constrained Nonlinear Problems

Numerical methods for solving general nonlinear constrained optimization problems are discussed in this chapter. A large number of methods and their variations are available in the literature for solving these problems. As is frequently the case with nonlinear problems, there is no single method that is clearly better than the others. Each method has its own strengths and weaknesses. The quest for a general method that works effectively for all types of problems continues. Most current journals and conferences on optimization contain new methods or refinements of existing methods for solving constrained nonlinear problems. A thorough review of all these developments is beyond the scope of this chapter. Instead, the main purpose of this chapter is to present the development of two methods that are generally considered among the best in their class, the ALPF (Augmented Lagrangian Penalty Function) method and the SQP (Sequential Quadratic Programming) method. For additional details refer to Fiacco [1983], Fiacco and McCormick [1968], Fletcher [1987], Gill, Murray, and Wright [1991], Gomez and Hennart [1994], McCormick [1983], Scales [1985], and Shapiro [1979].