An explosion is characterized as a sudden release of large energy over a very short duration. As the blast wave travels parallel to a surface, it creates a side-on pressure and when it hits a surface perpendicularly or at an angle, it creates a reflected pressure. Side-on pressure and reflected pressure are much higher than service loads for the structure. Thus, when a blast happens near a building that is not designed to withstand blast loads, it can cause catastrophic damage.
The objective of this study is to present a formulation for the design optimization of framed steel structures subjected to blast loads. Also, a formulation is presented for the design optimization of structures that can withstand some possible damage due to blast loads. To this end, an optimization procedure that includes definitions of design variables, cost function, constraints, and structural analyses is discussed. The design variables for beams and columns are the discrete values of the W-shapes selected from American Institute of Steel Construction (AISC) tables. The optimization problem is to minimize the total structural weight subjected to AISC strength requirements and blast design displacement constraints. Linear static, linear dynamic, and nonlinear dynamic analyses are incorporated in the optimization process and optimum designs are compared. Due to design variables and some constraints discontinuity, gradient-based optimization algorithms cannot be used to solve the optimization problem.
Therefore, metaheuristic algorithms are used that require only simulation results to solve problems with discrete variables and non-differentiable functions. Since the number of simulations and robustness to obtain good designs are important for the class of problems discussed in this research, a new hybrid optimization algorithm based on Harmony Search (HS) and Colliding Bodies Optimization (CBO) is developed and examined. The algorithm is named Hybrid Harmony Search - Colliding Bodies Optimization (HHC). Also, a novel design domain reduction technique is incorporated in HHC. Some benchmark discrete variable structural design problems are used to evaluate HHC. In comparison with some popular metaheuristic optimization algorithms, HHC is shown to be robust, effective, and needs fewer structural analyses to obtain the best designs.
Depending on the size of the structure to be designed, optimization of structures that require linear or nonlinear dynamic analyses using metaheuristic algorithms can be computationally expensive because these types of algorithms need large number of simulations to reach good designs. Equivalent Static Loads (ESL) approach, which has been used for optimization of structural systems subjected to dynamic loads using gradient-based algorithms, is examined for optimization of structures that have discrete design variables using metaheuristic algorithms. The proposed approach is named global optimization with equivalent static loads (GOESL). Solution of four numerical examples shows that GOESL can drastically reduce the number of dynamic analyses needed to reach the best design compared to an algorithm without the ESL approach. However, the ESL step alone cannot converge to the best design for the current formulation, even with many ESL cycles. Therefore, after a few ESL cycles, the procedure may switch to the original algorithm without the ESL cycles to improve designs further.
HHC and GOESL are used to solve three-dimensional framed steel structures subjected to blast loads with linear and nonlinear dynamic analyses as separate solution cases. The source of the blast loads is a car carrying 250 lbs of Trinitrotoluene (TNT) with 50 ft standoff distance from the front face of a 4-bay x 4-bay x 3-story building. Optimum designs of the structure to withstand blast loads show that penalty on the optimum structural weight is substantial when linear dynamic analysis is used. With nonlinear dynamic analysis, the penalty on the structural weight is substantially reduced. When the stiffness of the walls is included in the analysis model, there is very little penalty on the optimum structural weight with linear or nonlinear dynamic analysis models.
The best designs obtained with the linear and nonlinear dynamic analysis models are checked for some possible damages due to a blast. Two types of damage conditions are defined: (i) complete removal of some key members from the analysis model, and (ii) reduction of stiffness of some members. It is shown that the best designs using linear or nonlinear dynamic analyses can withstand all damage conditions. Thus, resilience of the designs to withstand blast loads is observed.