Shyh Rong Tzan

Convex model for seismic design of structures-I: Analysis

A convex model is used to estimate the maximum response of structural systems subjected to uncertain seismic excitations. The convex model is based on the assumption that the energy of the excitation is bounded . A reduction factor, defined in the modal domain by dividing the results obtained from the convex model by those from the time history of the actual record, is used to calibrate the convex model. An average reduction factor is also defined by averaging a set of excitation-specific reduction factors. The average reduction factor can be used for unknown excitations with an assumed energy bound and certain common earthquake characteristics. These common characteristics can be defined either by a set of previous earthquakes in the region or by regional earthquake spectra. The convex model using the average reduction factor yields acceptable predictions of the maximum response.

Optimal design of dynamically constrained structures

Abstract A modified iterated simulated annealing (MISA) method is proposed for optimal design of structural systems with dynamic constraints. The MISA method uses a random sequence of designs to find the optimal design. In performing the optimization, the MISA method employs two new features: the first is automatic reduction of the search region; and the second is sensitivity analysis of the design variables. The MISA method deviates from traditional annealing algorithms because of these two features and is considered to be a new method. A two-story frame structure with dynamic constraints was used in evaluating the performance of the MISA method. Classical optimal design methods were used to solve the same problem and the results were compared to MISA. The comparisons show that MISA is able to provide the global minimum even when infeasible initial designs are attempted. By contrast, some classical optimization methods either fail to converge or converge to local minima.

CONVEX MODEL FOR SEISMIC DESIGN OF STRUCTURES—II: DESIGN OF CONVENTIONAL AND ACTIVE STRUCTURES

The optimal design of the members of conventional structures or structures equipped with active bracing systems, known as active structures, is presented for uncertain excitations. Three approaches are used for obtaining the optimal structural design: (1) the time-history analysis of an actual earthquake record (AR), (2) the global energy-bound convex model adjusted with an excitation-specific reduction factor (RGEB), and (3) the global energy-bound convex model adjusted with an average reduction factor (ARGEB) for a set of excitations with common characteristics. The optimal structures obtained using the RGEB and ARGEB convex models have different sizes for their conventional members from the designs based on a time-history analysis of the actual earthquake (AR). The optimal design of the structure is carried out using a modified annealing algorithm. The advantage of using convex models to perform the optimization is that they represent a more general excitation than a single earthquake record. In addition, the RGEB and ARGEB convex models require considerably less computational effort since the constraints of the optimization become time-independent. A comparison between optimal designs of structures with conventional members only, and active structures indicates that the latter are more efficient by combining the conventional and active members.

Modified iterated simulated annealing algorithm for structural synthesis

Abstract A new hybrid simulated annealing method is presented for the optimization of structural systems subjected to dynamic loads. The optimization problem is formulated as a structural weight minimization, with time-varying constraints on floor displacements, velocities, accelerations, or floor drifts, and structural member combined stresses. In addition, time-invariant constraints on structural frequencies and member sizes that will satisfy the strong column–weak beam philosophy of the building codes can be imposed. The method uses elements of existing simulated annealing algorithms and introduces certain new procedures. Firstly, the search range is automatically reduced, by using the updated information of the current design, at each iteration. Secondly, the inner and outer iteration loops are implemented. Thirdly, sensitivity analysis of the time-varying global displacements is performed with respect to the design variables that are the structural member cross-sectional areas. The results of the sensitivity analysis identify which design variables must be modified to decrease the global displacements in the most effective manner. However, once the variables are identified from the sensitivity analysis, the new values of these variables are determined in a random manner. The possibility of attaining a global minimum is thus maintained. The method is suited for structural optimization problems with time-varying constraints because the annealing is a random search technique and can locate global rather than local minima.

Active structures considering energy dissipation through damping and plastic yielding

Abstract The optimal design of the conventional members of a building equipped with either passive or active control systems is presented for earthquake excitations. The optimized structure with structural control systems is known as an active structure. The influence of the structure’s inherent structural damping on the optimal design is included. The energy imparted to a structure designed so that its structural members would yield in a major earthquake is dissipated by damping and yielding. The inherent damping and yielding energy due to the conventional structural members, as well as the external damping energy from passive or active structural control are considered. The optimal design of viscoelastic dampers in terms of their number, location and cross-sectional area to achieve an increased effective damping is examined. Elastic and inelastic analyses of conventional and active structures are performed in which the number of yielding events, and the energy dissipation through damping and yielding are compared for different earthquakes. The structural control systems are found to assist in reducing the peak structural response and the number of yielding events.

Simulated annealing for the design of structures with time-varying constraints

The optimal design of structural systems with conventional members or systems with conventional as well as passive or active members is presented. The optimal sizes of the conventional members of structural systems are obtained for dynamic loads. A modified simulated annealing algorithm is presented which is used to solve the optimization problem with dynamic constraints. The present algorithm differs from existing simulated annealing algorithms in two respects; first, an automatic reduction of the search range is performed, and second, a sensitivity analysis of the design variables is utilized. The present method converges to the minimum in less iterations when compared to existing simulated annealing algorithms. The algorithm is advantageous over classical methods for optimization of structural systems with constraints arising from dynamic loads. For certain initial values of the design variables, classical optimization methods either fail to converge or produce designs which are local minima; the present algorithm seems to be successful in yielding the global minimum design.

Response to Arbitrarily Time-Varying Forces Using Convex Model

An energy-bound convex model is used to estimate the maximum structural response of single-degree-of-freedom and multiple-degree-of-freedom structural systems which are subjected to arbitrarily time-varying forces. Convex models specify uncertainties in the absence of detailed probabilistic information about the variables of interest. The concept of convex models provides an alternative way of analysis when a limited amount of information about the excitation is available. The subjective decisions which result when using convex models to incorporate uncertainty do not involve the element of chance. In general, convex models yield estimates of the maximum response that are conservative. In the present paper, equations for reduction factors are given for arbitrary time-varying forces of unknown shape. The reduction factors are independent of the value of the energy bound. The resulting predictions obtained by the reduced convex model estimates are within reasonable agreement to the maximum response obtained by time-history analysis of the arbitrarily time-varying forces.