Unknown Structural Response Research Articles

Multiscale topology optimization of cellular structures using Nitsche-type isogeometric analysis

This paper proposes a multiscale topology optimization method using Nitsche-type isogeometric analysis (IGA) for design of structures described by multiple non-uniform rational B-spline (NURBS) patches. In this method, at macroscale, unknown structural responses are calculated by Nitsche-type IGA, which not only ensures the consistency between geometric and analytical models, but also offers an effective way to enforce kinematic compatibility and mechanical equilibrium on interfaces between adjacent NURBS patches. At microscale, mechanical properties of microstructures are predicted by a Kriging metamodel at a low computational cost, which is constructed via some sample lattice unit cells (LUCs). In addition, analytical computation of sensitivities for coupled elements is developed. Finally, the structures are infilled by graded LUCs according to the density distribution within the design space. Some 2D and 3D numerical examples with conforming and non-conforming NURBS patches are presented to test the proposed method. Results indicate that the proposed method is effective for design of structures described by multiple NURBS patches.

Isogeometric topology and shape optimization for composite structures using level-sets and adaptive Gauss quadrature

The Level-Set Method (LSM) with the smooth and distinct description of structural boundaries offers more superior benefits for topology optimization. However, the classic Finite Element Method (FEM) and ersatz material method in the LSM cause numerical deficiencies in the optimization, such as iterative instability and the crispness loss of boundaries. This work focuses on developing an Isogeometric Topology and Shape Optimization (ITSO) method for the design of composite structures, in which a Non-Uniform Rational B-splines (NURBS)-based Multi-phase Level-Sets (NM-LS) model is constructed to present the distribution of multiple materials. The NM-LS model consists of an immersed representation using level-sets, NURBS parameterized level-sets and its development. Isogeometric Analysis (IGA) with adaptive Gauss quadrature method are applied to solve unknown structural responses, which can effectively remove several numerical artifacts resulting from the linear interpolation of ersatz material model in both design and analysis. Three models of structural geometry, numerical analysis and topology description can be integrated by the same NURBS basis functions, which can effectively improve numerical precision and iterative stability. Finally, several 2D and 3D numerical examples are addressed to demonstrate the effectiveness and efficiency of the proposed ITSO method on the design of composite structures.

Material similarity of scaled models

When different strain hardening, strain-rate sensitive and temperature softening materials are used for scaled model and prototype, the traditional similarity laws of solid mechanics will be broken. Although research works in the last twenty years have developed the correction methods of initial conditions to compensate for the similarity distortion, their basic correction factors are practically impeded for their inherent non-direct (depending on unknown structural responses) and inexact (having significant similarity errors) defects. In this paper, a more complete framework of material similarity is developed. Based on the similarity analysis of thermo-visco-plastic constitutive equation, the material dimensionless numbers are suggested to represent the objective similarity of strain hardening, strain-rate sensitive and temperature softening effects. The universal direct and exact solution of the basic correction factors is further proved when the material numbers of the scaled model and the prototype are equal, which overcomes the previous inherent defects radically. And the simple and practical phase diagram of ‘material numbers - strain/strain-rate/temperature’ curves are proposed to design the optimum similitude materials. Three impacted structure are numerically verified: circular plate, crooked plate, and Taylor bar. The results show that the proposed material numbers control the similarity behavior of different materials. When the proposed direct and exact methods are used by the designed optimum similitude materials, the completely different materials can behave acceptable exact similarity of strain, strain-rate, temperature, stress and displacement responses in time and space fields.

Time-Varying Wind Load Identification Based on Minimum-Variance Unbiased Estimation

A minimum-variance unbiased estimation method is developed to identify the time-varying wind load from measured responses. The formula derivation of recursive identification equations is obtained in state space. The new approach can simultaneously estimate the entire wind load and the unknown structural responses only with limited measurement of structural acceleration response. The fluctuating wind speed process is investigated by the autoregressive (AR) model method in time series analysis. The accuracy and feasibility of the inverse approach are numerically investigated by identifying the wind load on a twenty-story shear building structure. The influences of the number and location of accelerometers are examined and discussed. In order to study the stability of the proposed method, the effects of the errors in crucial factors such as natural frequency and damping ratio are discussed through detailed parametric analysis. It can be found from the identification results that the proposed method can identify the wind load from limited measurement of acceleration responses with good accuracy and stability, indicating that it is an effective approach for estimating wind load on building structures.

Application of Timoshenko beam theory to the estimation of structural response

Multi-story buildings are usually instrumented at a limited number of floors. Consequently, the structural response (e.g., acceleration, displacement) at the non-instrumented floors remains unknown and needs to be estimated using the acceleration data recorded at the instrumented floors. The prevailing way to estimate the unknown structural response is to interpolate the recorded data over the height of the building. Other methods such as the Mode Shape Based Estimation (MSBE) and Timoshenko Beam Based Estimation (TBBE) methods, on the other hand, use the mode shapes of bending, shear and Timoshenko beam modeling to estimate the unknown structural response. The Factor Building at the UCLA campus in Los Angeles, California, USA is utilized to test the performance of these methods, and the results are compared with conventional interpolation methods (e.g., linear or cubic spline interpolations). The results show clearly that both the MSBE and the TBBE methods provide a better estimation of unknown structural response than both linear interpolation methods.

A condition assessment method for time-variant structures with incomplete measurements

The structural damage incurred in a seismic event is always time-variant. In this paper, a new time-variant structural system identification method is proposed based on a two-stage strategy and incomplete structural acceleration responses. In the first stage, an external excitation identification method is developed for a time-variant structural system. The unknown structural response could be re-constructed with the average acceleration discrete algorithm in this stage. In the second stage, structural parameter is identified and updated with a reduced extended Kalman filter which can improve the computational effort. The re-constructed structural response and identified external excitation are used in the second stage for the damage identification and model updating. The proposed method is validated numerically with the simulation of a fifteen-storey shear frame structure subject to earthquake excitation. A model of a fourteen-storey concrete shear wall building was also studied experimentally with shaking table tests to further validate the proposed method. This shear wall building has a two-storey steel frame on top with base isolation. Both the stiffness of the model and the interface force in the isolator at the bottom of the steel frame during the seismic excitation were estimated with the proposed method. Results from both numerical simulations and laboratory tests indicate that the proposed method can be used to identify structural parameters and external excitations effectively based on a few number of polluted structural acceleration measurements.

Experimental Investigation of a Small-Scale Bridge Model under a Moving Mass

The dynamic response of a small-scale bridge model under a moving mass is investigated. The analysis is based on the continuous Euler–Bernoulli beam theory. By expanding the unknown structural response in a series of the beam eigenfunctions, the given problem is reduced to the solution of a set of second order linear differential equations with time varying coefficients. The analytical solution is validated through a series of experiments. A small-scale model is designed to satisfy both static and dynamic similitude with a selected prototype bridge structure, and a set of necessary similitude conditions for the given problem is provided. Attention is paid, in particular, to satisfaction of the mass similitude requirement, often constituting one of the main difficulties in the design of small-scale dynamic models. It is shown that experimental results are in good agreement with theoretical predictions, thus validating the analytical procedure.

Spline approximations for direct integration of structural dynamics

AbstractThe application of spline functions in the analysis of structural dynamics is presented in this paper. The nodal points in time discretization for determining the spline curve can be separated into two classes: the p nodal points before the current time (including current time) and the q nodal points after the current time. On the p nodal points, the structural responses were calculated at previous time steps. The q nodal points represent the unknown structural response at future time steps which should meet the requirement of dynamic equilibrium. By a trial and error procedure, at least 16 families of spline curves with different locations of p and q nodal points can be found to meet the requirements of unconditional stability. The accuracy of each family is dependent on the order of the spline and the locations of the nodal points. The 16 families of spline curves supply a wide range of accuracy that can be selected easily. It can be shown that the well‐known Wilson‐method and the Houbolt method are special cases of the present spline approximations.