Charles V. Camp

Design of Retaining Walls Using Big Bang–Big Crunch Optimization

A procedure is developed for designing low-cost or low-weight cantilever reinforced concrete retaining walls, with base shear keys, using big bang–big crunch (BB-BC) optimization. The objective of the optimization is to minimize the total cost or total weight per unit length of the retaining structure subjected to constraints on the basis of stability, bending moment, and shear force capacities and the requirements of the American Concrete Institute (ACI 318-05). An iterative population-based heuristic search method, BB-BC optimization has a numerically simple algorithm with relatively few control parameters as compared with other evolutionary methods. Low-cost and low-weight designs for two retaining walls are presented. In addition, results are presented on the effects of surcharge load, backfill slope, and internal friction angle of the retained soil on the values of low-cost and low-weight designs with and without a base shear key.

Overhauser elements in boundary element analysis

The accuracy and the merit of the Overhauser cubic spline as an isoparametric representation in solving two-dimensional potential problems by the boundary element method (BEM) is investigated. The Overhauser parametric shape functions are used to form a curvilinear boundary element which is intrinsically C^1-continuous between elements. The resulting Overhauser element avoids the computational inefficiencies suffered by general cubic splines that require an additional variable to enforce derivative continuity between elements. Several numerical examples of phenomena governed by both the Poisson and biharmonic equations are presented and compared with existing numerical results or exact solutions.

Boundary element analysis of nonhomogeneous biharmonic phenomena

1. Boundary Elements and the Biharmonic Equation.- 2. Two-Dimensional Biharmonic Phenomena.- 3. Element Types for Boundary Discretization.- 4. Domain Discretization and Internal Point Calculations.- 5. Example Analyses.- 6. Computer Program.- 7. General Summary and Concluding Remarks.- References.

Optimal design of truss structures for size and shape with frequency constraints using a collaborative optimization strategy

A collaborative parallel optimization strategy is proposed.A higher-level TLBO algorithm called school-based optimization is developed.Size and shape optimization under frequency constraints is addressed.Comparative studies illustrate the superiority of the proposed algorithm. A new metaheuristic strategy is proposed for size and shape optimization problems with frequency constraints. These optimization problems are considered to be highly non-linear and non-convex. The proposed strategy extends the idea of using a single optimization process to a series of collaborative optimization processes. In this study, a modified teaching-learning-based optimization (TLBO), which is a relatively simple algorithm with no intrinsic parameters controlling its performance, is utilized in a collaborative framework and introduced as a higher-level TLBO algorithm called school-based optimization (SBO). SBO considers a school with multiple independent classrooms and multiple teachers with inter-classroom collaboration where teachers are reassigned to classrooms based on their fitness. SBO significantly improves the both exploration and exploitation capabilities of TLBO without increasing the algorithms complexity. In addition, since the SBO algorithm uses multiple independent classrooms with interchanging teachers, the algorithm is less likely to be influenced by local optima. A parametric study is conducted to investigate the effects of the number of classes and the class size, which are the only parameters of SBO. The SBO algorithm is applied to five benchmark truss optimization problems with frequency constraints and the statistical results are compared to other optimization techniques in the literature. The quality and robustness of the results indicate the efficiency of the proposed SBO algorithm.

A boundary element method for viscous flows at low Reynolds numbers

Abstract Solutions are presented for the nonlinear biharmonic equation describing steady, two-dimensional viscous flow of an incompressible fluid at low Reynolds number. The governing equation for the flow field is reformulated into a set of coupled nonlinear Poisson-type boundary integral equations. The degree of accuracy of the solution, as compared to existing procedures for this problem, is improved by using linear isoparametric elements combined with analytic expressions for the piecewise integration of the fundamental function and its derivatives over each element. Analytic integration is used to eliminate errors introduced by using Gaussian quadrature, especially those errors associated with internal value calculations very near the boundary. At zero Reynolds number the coupled integral equations are linear, giving rise to a formulation in which it is necessary only to evaluate boundary integrals. At nonzero Reynolds numbers the nonlinear character of the integral equations requires an iterative solution technique and introduces domain integrations that are calculated using an improved volume quadrature method, thereby avoiding the disadvantges associated with explicit domain cell methods. Numerical solutions of the integral formulation are presented in terms of plots of the streamlines at various Reynolds numbers and for several domain geometries.

Particle Swarm Optimization for The Design of Trusses

Particle swarm optimization (PSO) is applied to the low-weight design of trusses. The objective function considered is the total weight (or cost) of the structure subjected to stress and displacement constraints. Traditionally, PSO has been applied to unconstrained problems; in this application, a hybrid PSO procedure incorporates a penalty function to account for stress and displacement constraints. In addition, the hybrid PSO procedure includes a search space reduction strategy that attempts to focus the search in the near-vicinity of the best solution found. The effectiveness of the hybrid PSO design procedure is demonstrated with several examples and compared with other classical optimization methods.

Constructing subsurface profiles using GIS

Abstract A geographic information system (GIS) macro procedure for creating subsurface profiles from well log data is developed. The well log data base is constructed from interpretation of a series of borehole geophysical logs. The GIS procedure targets a modelling area and interpolates the well data base to create a three-dimentional representation of the subsurface environment. Any number of cross-sectional profiles or three-dimensional images of well log data may be created and viewed interactively. The resulting profiles provide basic geometric data for ground water flow and contaminant transport models. A brief introduction to the ARC/INFO system, emphasizing the attributes of the data structure and the macro language, is given. Several subsurface profiles of Shelby County, Tennessee are developed using the GIS profile procedure.

Minimization of CO2 Emissions for Spread Footings under Biaxial Uplift Using a Big Bang-Big Big Crunch Algorithm

A procedure is developed to minimize CO2 emissions for the design of reinforced concrete spread footings subjected to biaxial bending satisfying both geotechnical limit states and structural requirements using a Big Bang-Big Crunch (BB-BC) algorithm. The objectives are to minimize CO2 emissions and compare designs developed for loading outside of the kern area with analysis procedures when loading is within the kern area. The CO2 emissions are associated with the extraction and transportation of raw materials; processing, manufacturing, and fabrication of products; and the emissions of equipment involved in the construction process. The CO2 objective function is subjected to soil bearing and displacement limits, as well as bending moment, shear force, and reinforcing details specified by the American Concrete Institute (ACI 318-11). A design example is presented to compare low-CO2 emission designs when detachment of the soil from the footing occurs to low-CO2 emission designs when the entire base of the footing is in compression. Results are presented that demonstrate the effects of different magnitudes of eccentricities on designs.

Boundary Elements and Perturbation Theory for Vibrating Plates

In this work, classical techniques from perturbation theory will be applied to develop a boundary integral formulation for low frequency forced vibrations of elastic plates. The functional form of the applied load and the plate deflection are assumed to be products of a temporal function and corresponding spatial functions. The separation of variables approach removes the difficulties associated with transient analysis. The resulting boundary element formulation requires consecutive solutions to a set of coupled non-homogeneous biharmonic equations. The domain integral normally associated with each non-homogeneous equation is transformed to a set of boundary integrals using the Rayleigh-Green identity. Numerical solutions of the perturbation-based expansion equations of forced vibrations using the boundary element method (BEM) are presented and compared with analytical analysis.

A boundary oriented domain quadrature technique for arbitrary multiply-connected regions

Abstract An innovative two-dimensional domain quadrature technique inherently sensitive to functions which develop a singularity within the integration region is developed. The quadrature method utilizes a finite set of points located along the boundary and connected into a series of elements to represent the domain geometry, a feature which makes it extremely convenient for BEM work. The method combines the convenience of high order Gaussian quadrature with the practical advantages of implicit discretization of the domain. The application of the technique is to be illustrated with several useful examples of interest to engineers.