محدود تجزیه و تحلیل حساسیت پاسخ عنصر: یک مقایسه بین مدل های عنصر چارچوب قدرت محور و مبتنی بر جابجایی

This paper focuses on a comparison between displacement-based and force-based elements for static and dynamic response sensitivity analysis of frame type structures. Previous research has shown that force-based frame elements are superior to classical displacement-based elements enabling, at no significant additional computational costs, a drastic reduction in the number of elements required for a given level of accuracy in the simulated response. The present work shows that this advantage of force-based over displacement-based elements is even more conspicuous in the context of gradient-based optimization methods, which are used in several structural engineering sub-fields (e.g., structural optimization, structural reliability analysis, finite element model updating) and which require accurate and efficient computation of structural response and response sensitivities to material and loading parameters. The two methodologies for displacement-based and force-based element sensitivity computations are compared. Three application examples are presented to illustrate the conclusions. Material-only non-linearity is considered. Significant benefits are found in using force-based frame element models for both response and response sensitivity analysis in terms of trade-off between accuracy and computational cost.

In recent years, great advances in the non-linear analysis of frame structures were led by the development of force-based elements, which have been found superior to classical displacement-based elements in tracing material non-linearities such as those encountered in steel, reinforced concrete, and composite frame structures (see [12], [13], [14] and [15]). The state-of-the-art in computational simulation of frame structures subjected to static and dynamic loads is in the non-linear domain to capture the complex behavior of structural systems when approaching their failure range. Maybe even more important than the simulated non-linear response of a frame structure is its sensitivity to various geometric, mechanical, and material properties defining the structure and to loading parameters. Significant research has been devoted to the general problem of design sensitivity analysis (see [1], [2], [16] and [17]). Consistent finite element response sensitivity analysis methods are already well established for displacement-based finite elements (see [4], [6], [10] and [18]). More recently, a procedure for response sensitivity computation using force-based frame elements has been developed [5] by the authors. This new procedure allows the use of force-based frame elements as a powerful simulation tool in applications which require finite element response sensitivity analysis results. Finite element response sensitivities represent an essential ingredient for gradient-based optimization methods needed in structural reliability analysis, structural optimization, structural identification, and finite element model updating (see [7] and [10]). This paper presents a careful comparison between the response sensitivity computation methodologies for force-based and displacement-based frame elements in the context of materially-non-linear-only analysis. Both material and discrete loading parameters are considered. Three application examples involving quasi-static and dynamic loadings illustrate the different features of the two formulations in terms of computational effort and accuracy. Consistent finite element response sensitivities are compared with analytical (exact) when available. Conclusions are drawn about the relative merits of the displacement-based and force-based approaches for finite element response sensitivity analysis.

This paper presents an accurate and insightful comparison of the procedures for computing response sensitivities to material and discrete loading parameters for displacement-based and force-based materially-non-linear-only finite element models of structural frame systems. Both procedures emanate from the direct differentiation method, and consist of differentiating exactly the incremental-iterative numerical scheme for the finite element response calculation. Comparison of their implementation in a general-purpose non-linear finite element analysis program based on the direct stiffness method is discussed in great detail. Three representative application examples are provided: a cantilever steel beam and a simple statically indeterminate frame both subjected to a non-linear quasi-static pushover analysis, and a five-storey, one-bay steel moment-resisting frame subjected to a non-linear dynamic analysis for earthquake base excitation. Closed-form solutions for the response and response sensitivities are available for the first two examples. The non-linear inelastic material model used in the examples consists of the 1-D J2 plasticity model, which describes the moment–curvature constitutive law at the section level. However, the differentiation methods compared in this paper apply to any material constitutive model that can be formulated analytically. Based on the results presented, it is concluded that the established superiority of force-based (F-B) over displacement-based (D-B) frame elements in terms of trade-off between accuracy in response computations and computational effort is even emphasized for response sensitivity analysis. While for D-B frame element models a significant refinement of the finite element mesh is necessary in order to obtain accurate response sensitivity results, in the case of F-B frame element models, the mesh used for accurate response computation also provides satisfactory response sensitivity results. The superiority of F-B over D-B elements established in this paper for finite element response sensitivity analysis could have significant impact on any kind of applications that requires response sensitivity analysis. Such applications include structural reliability analysis, structural optimization, structural identification, and finite element model updating.