Franz Bamer

An efficient response identification strategy for nonlinear structures subject to nonstationary generated seismic excitations

ABSTRACT The Monte Carlo method is computationally demanding. Consequently, applying that method to high-dimensional nonlinear systems is practically not feasible. Therefore, a new strategy is proposed in this article, which enables the evaluation of the response statistics of high-dimensional structures subject to random seismic excitations in a nonlinear reduced low-order subspace. It is shown that the new model order reduction method provides the possibility to overcome the computational issue of large-scale Monte Carlo simulations. It provides reliable approximations of the response statistics, when compared with those of the non-reduced Monte Carlo method.

A new model order reduction strategy adapted to nonlinear problems in earthquake engineering

Summary Earthquake dynamic response analysis of large complex structures, especially in the presence of nonlinearities, usually turns out to be computationally expensive. In this paper, the methodical developments of a new model order reduction strategy (MOR) based on the proper orthogonal decomposition (POD) method as well as its practical applicability to a realistic building structure are presented. The seismic performance of the building structure, a medical complex, is to be improved by means of base isolation realized by frictional pendulum bearings. According to the new introduced MOR strategy, a set of deterministic POD modes (transformation matrix) is assembled, which is derived based on the information of parts of the response history, so‐called snapshots, of the structure under a representative earthquake excitation. Subsequently, this transformation matrix is utilized to create reduced‐order models of the structure subjected to different earthquake excitations. These sets of nonlinear low‐order representations are now solved in a fractional amount of time in comparison with the computations of the full (non‐reduced) systems. The results demonstrate accurate approximations of the physical (full) responses by means of this new MOR strategy if the probable behavior of the structure has already been captured in the POD snapshots. Copyright

A Structural Pounding Formulation Using Systematic Modal Truncation

The evaluation of the response function of the structural pounding problem is generally time-consuming if high-order systems are applied. The well-known modal truncation strategy is outstandingly efficient for a single linear ground-accelerated structure. However, for the analysis of the structural pounding problem, the classical modal truncation technique turns out to be ineffective as additional higher frequency motion due to possible contact impact occurs. This makes the determination of how many modes should be taken into account in order to obtain a required level of accuracy more difficult. Therefore, in this paper, a systematically controlled modal truncation strategy adapted to the seismic pounding formulation under consideration of high nonlinearity and nonsmoothness of contact problems is introduced. A comparative study of the classical and the controlled modal truncation technique is presented and a comparison with the commercial software package ABAQUS© is provided. It is shown that the computational accuracy is significantly improved when applying the new systematically controlled modal truncation strategy.

A Nonlinear Deterministic Mode Decomposition Strategy for High-Dimensional Monte Carlo Simulations: A Nonlinear Deterministic Mode Decomposition Strategy for High-Dimensional Monte Carlo Simulations

Generally, Monte Carlo (MC) simulations of high-dimensional nonlinear systems are practically unrealizable. Therefore, equivalent linearization techniques [1] or weighted simulation methods [2] are proposed to handle this issue. In this paper, we present a reduced MC simulation strategy for high-order systems that is executed in a nonlinear reduced subspace. The main goal is to identify one representative transformation matrix that is applied to all sample computations within the MC simulation run. Thus, we propose an a-priori response identification by computation of the response of the structure excited by one representative sample event in the physical coordinate, that is to say an evaluation of representative snapshots. The proper orthogonal decomposition (POD) (e.g. [3–5]) is applied to evaluate the determinstic transfromation matrix (POD modes) into the POD subspace. Subsequently, each sample response is evaluated in this low-order POD subspace within a fractional amount of computational effort.

AN EFFICIENT ORDER REDUCTION STRATEGY IN EARTHQUAKE NONLINEAR RESPONSE ANALYSIS OF STRUCTURES

Since earthquake dynamic response analysis of large and complex structures are computationally time demanding, efficient methods that can reduce the system order are of high interest. In this sense, there are different methods available, which try to provide a proper equivalent model. However, in the presence of nonlinearities in the structural elements, most of those methods are ruled out due to their linear assumptions. Therefore, this contribution aims at providing an efficient strategy, which can reduce the order of the nonlinear structural model while retaining important structural characteristics for further earthquake dynamic response analysis. The model order reduction (MOR) strategy is developed based on the proper orthogonal decomposition (POD) method to derive a set of nonlinear deterministic POD modes according to the information of the response history (snapshots) of the full order structure under one or a set of representative earthquake excitations. Subsequently, the POD modes are utilized to create the reduced-order models of the structure subjected to different earthquake excitations. Then, the reduced order models need substantially less amount of computational time in comparison to the full order models. This study presents the application results of the introduced new strategy to a realistic building structure, which is base-isolated by means of frictional bearing elements for better seismic performance. The results demonstrate accurate approximations of the physical (full) responses by means of this new MOR strategy if the probable behavior of the structure has already been captured in the POD snapshots.