Quan Gu

Coupling of a 3D Finite Element Model of Cardiac Ventricular Mechanics to Lumped Systems Models of the Systemic and Pulmonic Circulation

In this study we present a novel, robust method to couple finite element (FE) models of cardiac mechanics to systems models of the circulation (CIRC), independent of cardiac phase. For each time step through a cardiac cycle, left and right ventricular pressures were calculated using ventricular compliances from the FE and CIRC models. These pressures served as boundary conditions in the FE and CIRC models. In succeeding steps, pressures were updated to minimize cavity volume error (FE minus CIRC volume) using Newton iterations. Coupling was achieved when a predefined criterion for the volume error was satisfied. Initial conditions for the multi-scale model were obtained by replacing the FE model with a varying elastance model, which takes into account direct ventricular interactions. Applying the coupling, a novel multi-scale model of the canine cardiovascular system was developed. Global hemodynamics and regional mechanics were calculated for multiple beats in two separate simulations with a left ventricular ischemic region and pulmonary artery constriction, respectively. After the interventions, global hemodynamics changed due to direct and indirect ventricular interactions, in agreement with previously published experimental results. The coupling method allows for simulations of multiple cardiac cycles for normal and pathophysiology, encompassing levels from cell to system.

Handling of Constraints in Finite-Element Response Sensitivity Analysis

In this paper, the direct differentiation method (DDM) for finite-element (FE) response sensitivity analysis is extended to linear and nonlinear FE models with multi-point constraints (MPCs). The analytical developments are provided for three different constraint handling methods, namely: (1) the transformation equation method; (2) the Lagrange multiplier method; and (3) the penalty function method. Two nonlinear benchmark applications are presented: (1) a two-dimensional soil-foundation-structure interaction system and (2) a three-dimensional, one-bay by one-bay, three-story reinforced concrete building with floor slabs modeled as rigid diaphragms, both subjected to seismic excitation. Time histories of response parameters and their sensitivities to material constitutive parameters are computed and discussed, with emphasis on the relative importance of these parameters in affecting the structural response. The DDM-based response sensitivity results are compared with corresponding forward finite difference analysis results, thus validating the formulation presented and its computer implementation. The developments presented in this paper close an important gap between FE response-only analysis and FE response sensitivity analysis through the DDM, extending the latter to applications requiring response sensitivities of FE models with MPCs. These applications include structural optimization, structural reliability analysis, and finite-element model updating.

Performance and Risk Assessment of Soil-Structure Interaction Systems Based on Finite Element Reliability Methods

In the context of performance-based earthquake engineering, reliability method has been of significant importance in performance and risk assessment of structures or soil-structure interaction (SSI) systems. The finite element (FE) reliability method combines FE analysis with state-of-the-art methods in reliability analysis and has been employed increasingly to estimate the probability of occurrence of failure events corresponding to various hazard levels (e.g., earthquakes with various intensity). In this paper, crucial components for FE reliability analysis are reviewed and summarized. Furthermore, recent advances in both time invariant and time variant reliability analysis methods for realistic nonlinear SSI systems are presented and applied to a two-dimensional two story building on layered soil. Various time invariant reliability analysis methods are applied, including the first-order reliability method (FORM), importance sampling method, and orthogonal plane sampling (OPS) method. For time variant reliability analysis, an upper bound of the failure probability is obtained from numerical integration of the mean outcrossing rate (MOCR). The MOCR is computed by using FORM analysis and OPS analysis. Results by different FE reliability methods are compared in terms of accuracy and computational cost. This paper provides valuable insights for reliability based probabilistic performance and risk assessment of SSI systems.

New Multidimensional Visualization Technique for Limit-State Surfaces in Nonlinear Finite-Element Reliability Analysis

Structural reliability problems involving the use of advanced finite-element models of real-world structures are usually defined by limit-states expressed as functions (referred to as limit-state functions) of basic random variables used to characterize the pertinent sources of uncertainty. These limit-state functions define hyper-surfaces (referred to as limit-state surfaces) in the high-dimensional spaces of the basic random variables. The hyper-surface topology is of paramount interest, particularly in the failure domain regions with highest probability density. In fact, classical asymptotic reliability methods, such as the first- and second-order reliability method (FORM and SORM), are based on geometric approximations of the limit-state surfaces near the so-called design point(s) (DP). This paper presents a new efficient tool, the multidimensional visualization in the principal planes (MVPP) method, to study the topology of high-dimensional nonlinear limit-state surfaces (LSSs) near their DPs. The MVPP method allows the visualization, in particularly meaningful two-dimensional subspaces denoted as principal planes, of actual high-dimensional nonlinear limit-state surfaces that arise in both time-invariant and time-variant (mean out-crossing rate computation) structural reliability problems. The MVPP method provides, at a computational cost comparable with SORM, valuable insight into the suitability of FORM/SORM approximations of the failure probability for various reliability problems. Several application examples are presented to illustrate the developed MVPP methodology and the value of the information provided by visualization of the LSS.

Extension of the DP‐RS‐Sim Hybrid Method to Time‐Variant Structural Reliability Analysis

This paper presents the extension to time‐variant reliability applications of a novel hybrid reliability method, namely the Design Point—Response Surface—Simulation (DP‐RS‐Sim) method. This method combines in an innovative way the design point search used in First‐ and Second‐Order Reliability Methods (FORM/SORM) with the response surface method and appropriate simulation techniques. The proposed method is illustrated by using as benchmark example a nonlinear inelastic single‐degree‐of‐freedom system subjected to Gaussian white noise base excitation from at rest initial conditions. The system is considered to fail when the roof displacement exceeds a predefined deterministic threshold. Estimates of the time‐variant failure probability obtained through the DP‐RS‐Sim method are compared with the FORM‐based mean out‐crossing rate computations and crude Monte Carlo simulation results considered as reference solution. It is found that the DP‐RS‐Sim method can provide accurate time‐variant failure probability estimates at low computational cost compared to other existing structural reliability methods and is therefore a promising method for large scale time‐variant reliability applications.

Finite element response sensitivity analysis of three-dimensional soil-foundation-structure interaction (SFSI) systems

The nonlinear finite element (FE) analysis has been widely used in the design and analysis of structural or geotechnical systems. The response sensitivities (or gradients) to the model parameters are of significant importance in these realistic engineering problems. However the sensitivity calculation has lagged behind, leaving a gap between advanced FE response analysis and other research hotspots using the response gradient. The response sensitivity analysis is crucial for any gradient-based algorithms, such as reliability analysis, system identification and structural optimization. Among various sensitivity analysis methods, the direct differential method (DDM) has advantages of computing efficiency and accuracy, providing an ideal tool for the response gradient calculation. This paper extended the DDM framework to realistic complicated soil-foundation-structure interaction (SFSI) models by developing the response gradients for various constraints, element and materials involved. The enhanced framework is applied to three-dimensional SFSI system prototypes for a pile-supported bridge pier and a pile-supported reinforced concrete building frame structure, subjected to earthquake loading conditions. The DDM results are verified by forward finite difference method (FFD). The relative importance (RI) of the various material parameters on the responses of SFSI system are investigated based on the DDM response sensitivity results. The FFD converges asymptotically toward the DDM results, demonstrating the advantages of DDM (e.g., accurate, efficient, insensitive to numerical noise). Furthermore, the RI and effects of the model parameters of structure, foundation and soil materials on the responses of SFSI systems are investigated by taking advantage of the sensitivity analysis results. The extension of DDM to SFSI systems greatly broaden the application areas of the d gradient-based algorithms, e.g. FE model updating and nonlinear system identification of complicated SFSI systems.

Development of Collaborative Structure Analysis (CSA) System and Its Application to Investigate Effects of Soil-Structure Interaction

In this article, a collaborative structure analysis (CSA) system is developed for integrating different finite-element simulation programs. In this system, a simulated structure is divided into multiple substructures, and the interaction between the substructures is considered. Interfaces for the commercial finite-element program ABAQUS and for an open-source framework for structure analysis, OpenSees, are developed to achieve CSA integration. The CSA system is applied to analysis of a soil-structure interaction (SSI) problem, and the effects of SSI are investigated, and the efficiency and accuracy of the system are demonstrated.

Performance Assessment of a Concrete Gravity Dam at Shenwo Reservoir of China Using Deterministic and Probabilistic Methods

NSFC [51261120376, 11102174, 51281220267]; Open Research Fund Program of State key Laboratory of Hydroscience and Engineering [sklhse-2013-C-02]; Administration department of Shenwo Reservoir