Structural model correlation using large admissible perturbations incognate space

Abstract

A nonlinear perturbation method is developed to solve the problem of correlating a finite element model (FEM) to a structure for which an incomplete set of natural frequencies and mode shapes and/or some static deflections have been measured. The solution algorithm can handle differences between FEM and structure, in design variables and response, as large as 100-300%, depending on the scale of the structure and correlation measures. This is achieved incrementally by making inadmissible predictions, identifying the modal cognate space relevant to the correlation measures, and making admissible corrections in the cognate space. The developed computer code postprocesses results of the FEM modal and/or static analyses of the initial model only. No additional finite element analysis is required. Lagrange multipliers reveal the dominant correlation requirements and the active admissible cognate subspace. Depending on the number of correlation variables and measures, an optimal, a unique, or an inadmissible minimal error solution may be produced. Beam and offshore tower examples are used to test the algorithm and investigate conflicting requirements, definition of admissible cognate space, limits of allowable differences between FEM and structure, accuracy, and cost of the nonlinear perturbation method.

Topology redesign for performance by large admissible perturbations

“…assuming that f = { f }. If this is not the case, as in hydrodynamic loading of offshore platforms, see Bernitsas and Tawekal (1991). Let {Q´} be the transformed displacement vector, which is defined as…”

“…These two objectives were integrated by Kim and Bernitsas (1990) for redesign, satisfying both objectives simultaneously. Bernitsas and Tawekal (1991) solved the problem of model calibration by LEAP in a cognate space. Stiffened plate and shell elements were added by Bernitsas and Rim (1994).…”

Topology and performance redesign of complex structures by large admissible perturbations

“…Validity of linear perturbation and sensitivity methods, however, is limited to small structural changes between S1 and S2 (Stetson 1975;Stetson and Harrison 1981;Sandstrom and Anderson 1982). Nonlinear perturbation methods were developed allowing for large structural changes-on the order of 100% to 300% from the initial State S1-by implementing predictor-corrector solution schemes (Bernitsas and Kang 1991;Bernitsas and Tawekal 1991;Bernitsas and Rim 1994;Beyko and Bernitsas 1993;Hoff and Bernitsas 1985;Kang et al 1992;Kang and Bernitsas 1994;Kim and Bernitsas 1990;Hoff and Bernitsas 1986).…”

“…The relation between the two States S1 and S2 is highly nonlinear. The LargE Admissible Perturbation (LEAP) theory was developed to formulate and solve redesign problems (Bernitsas and Kang 1991;Bernitsas and Tawekal 1991;Bernitsas and Rim 1994;Beyko and Bernitsas 1993).…”

“…LEAP can solve large change redesign problems without resorting to sensitivity or linearization. LEAP has been used successfully to solve various practical problems in structural analysis and design such as model reduction (Kang et al 1992), model correlation (calibration) (Bernitsas and Tawekal 1991), and reliability (Beyko and Bernitsas 1993) using static, dynamic, and/ or stress constraints. The changes between S1 and S2 can be as large as 100%-300%, depending on the scale and characteristics of the finite element model.…”