Journal of Engineering Mechanics

This work provides a Bayesian reinterpretation of model falsification. We show that model falsification can be viewed as an approximate Bayesian computation (ABC) approach when hypotheses (models) are sampled from a prior. To achieve this, we recast model falsifiers as discrepancy metrics and density kernels such that they may be adopted within ABC and generalized ABC (GABC) methods. We call the resulting frameworks model-falsified ABC and model-falsified GABC, respectively. As a result of our reinterpretation, the set of unfalsified models can be shown to be realizations of an approximate posterior. We consider both error- and likelihood-domain model falsification. Model-falsified (G)ABC is used to address two practical types of inverse problems, although with synthetic measurements. The first two problems concern parameter estimation and include applications of ABC to the inference of a statistical model in which the likelihood can be difficult to compute, and the identification of a cubic-quintic dynamical system. The third example involves model selection for the base isolation system of a four-degree-of-freedom base-isolated structure. The performance of model-falsified ABC and GABC is compared with that of Bayesian inference. The results show that model-falsified (G)ABC can be used to solve inverse problems in a computationally efficient manner. The results are also used to compare the various falsifiers in terms of their capability to approximate the posterior and some of its important statistics. Furthermore, we show that model falsifier–based density kernels can be used in kernel regression to infer unknown model parameters and compute structural responses under epistemic uncertainty.

According to the governing wave equations for unsaturated porous media, a theoretical model is proposed to obtain the transient response solution of single-layer unsaturated porous media in one-dimensional conditions with general boundary conditions and arbitrary initial conditions when subjected to arbitrary vertical load. Parameters total stress $\sigma$, absolute soil displacement $u$, wetting fluid pressure $p_w$, relative displacement $w$, nonwetting fluid pressure $p_n$, and relative displacement $v$, which are independent of each other, are suggested firstly to express the boundary conditions through a linear combination method in pairs. Various boundary conditions can be obtained through adjusting the linear combination parameters. By utilizing the variable separation method, the eigenvalues and eigenfunctions of the undamped characteristic equation are obtained. Through the method of undetermined coefficients and orthogonality of eigenfunctions, the transient response problem can be converted to an initial value problem, which includes a series of ordinary differential equations. By making use of the precise time-integration method modified by the authors, the semianalytical solutions can finally be approached. Compared with existing research, the semianalytical solutions of this study are more general and can be exactly degenerated into some other boundary conditions. The validity of this method is verified by comparing the results with the current literature. Then, several examples are carried out to study the transient responses characteristic of unsaturated porous media subjected to the step load. The results demonstrate that there are three kinds of compression wave in the dynamic response of unsaturated porous media. In a short time, the semipermeable condition results are similar to permeable and impermeable conditions. However, results become complex over a long time due to the reflection and superposition of the compression waves.

This paper presents a stochastic analysis of the size effect on the nominal strength of quasibrittle structures with a large preexisting notch. This type of scaling behavior has been extensively studied within a deterministic framework. Little attention is paid to stochastic analysis, which is essential for reliability-based analysis and design of engineering structures. Stochastic finite element simulations are performed to study the failure of geometrically similar beams of different sizes. The numerical analysis uses a continuum damage model, in which the tensile strength and fracture energy are modeled by homogeneous random fields. Different correlation lengths are considered as a parametric study. The analysis yields the size effects on the mean and coefficient of variation (CoV) of the nominal structural strength. It is shown that the size effect on the mean strength agrees well with the Bazant size effect model. The simulation predicts a strong size effect on the CoV of the nominal strength. Small-, intermediate-, and large-size asymptotes are derived analytically for the scaling behavior of the strength CoV. Based on these asymptotes, an approximate scaling equation is proposed for the CoV of nominal strength. The effect of the correlation length on the simulated failure behavior is discussed.

Abstract

Architected materials are a new class of materials that interlink practices in architecture and structural engineering to produce materials by conjugation of several simple materials through the interplay between geometry and material properties. Tensegrity structures are composed of struts and cables held in a state of self-stress. With a high strength-to-weight ratio, they provide opportunities for deployable and transportable bridges. Although tensegrity structures are indeterminate, cable damage is challenging to predict and detect a priori, which is aided by a resilient architected material segment as a structural health indicator. The technology of 3D printing complements the development of architected material. Computational studies have shown the effect of coordination number and cross-linking density on the stretch behavior of polymer networks for microscopic deformation scale. This paper presents the relationship between various parameters of multilayered randomized architected material (MLRAM) and its tensile behavior. The randomization of link orientation is to address the unknown direction of the critical force in the strut. A computational model calibrated through experimental testing was developed that mimics the tensile behavior of MLRAM. Using this model, the variation in the tensile behavior in terms of peak tensile capacity and postpeak behavior of MLRAM can be studied for various geometries with specific parameters. From the study, it is observed that the tensile capacity and stiffness of the MLRAM increase with a higher coordination number.

Practical Applications

The recent advancement of additive manufacturing and 3D printing have provided researchers with the scope to study the feasibility of many difficult geometries and its properties. This is one such study that develops and investigates the tensile properties of a newly developed multilayered randomized architected material (MLRAM). The tensile properties were determined experimentally for centimeter-scale 3D-printed models and a computational model was proposed to replicate the behavior in the linear static region. This novel study provides a preliminary idea of a new concept of architected material that can be extended to a three-dimensional concept in the future. First, the model helps researchers investigate various geometry and design materials with properties as required for specific applications. This proposed MLRAM extended into a three-dimensional material also has the potential to act as visual damage detection indicators that can be incorporated in highly redundant structural systems such as tensegrity structures.

The behavior of axisymmetric cylinders under various surface loading has remained the topic of research for many years. Most of the solutions presented in the literature are load-specific. Therefore a general solution is sought to satisfy any boundary conditions prescribed on any surface. This paper presents a general solution to satisfy a wide combination of boundary conditions prescribed on the curved as well as on the flat ends of a cylinder. A hollow cylinder was considered, composed of transversely isotropic material. The formulation is based on the variational principle, resulting in a set of coupled governing equations and associated boundary conditions. The solutions to the coupled governing partial differential equations are obtained by systematically decoupling them, followed by the method of separation of variables and the Frobenius method. All the boundary conditions are satisfied by making use of either the Fourier or the Fourier–Bessel transformation. The solutions for various test cases were validated by comparing them against three-dimensional solutions obtained using finite-element analysis. The solution for the solid cylinder was obtained by considering the limiting case of the internal radius approaching Zero.

A frequency-domain finite element method and boundary element method (FEM-BEM) coupled numerical method is presented to investigate the dynamic responses of a fluid-filled lined tunnel buried in the ground. The fluid is modeled as an inviscid and compressible liquid, the lining is mimicked as an elastic hollow cylinder, and the ground is modeled as an elastic medium. Initially, based on the Laplace transform and Galerkin method, dynamic governing equations of fluid and those of lining are solved. Meanwhile, dynamic governing equations of ground are solved using methods of Laplace transform, and Helmholtz decomposition together with a reciprocal theorem. In the following stage, fluid, lining, and ground are coupled and solved successfully according to conditions of deformation compatibility and force balance on their interfaces. The solutions in the time domain are obtained with the aid of the inverse Laplace transform. Comparisons with previous studies have validated the proposed numerical method. The dynamic water pressure inside the tunnel and the dynamic radial displacement of the lining under the water hammer are obtained. It is concluded that ignoring the effect of ground may overestimate the magnitude of lining radial displacements and inaccurately evaluate the axial distribution of the displacement. When the stiffness ratio of ground to lining exceeds a certain critical level, the displacement dramatically reduces.

The numerical modeling of thermomechanical fracture is an essential aspect of designing critical components in various industries, including aerospace, automobile, and nuclear. The phase-field method is a suitable approach for simulating thermomechanical fracture problems. However, this method can be computationally expensive. In this study, we propose a multilevel adaptive mesh refinement (ML-AMR) using a phase-field approach, for thermomechanical fracture problems. The proposed approach can efficiently and accurately capture the crack topology without the need for any pre-refinement or explicit marking of damage boundary. Our proposed ML-AMR algorithm introduces an error estimator based on effective crack driving energy computed based on thermomechanical loading using the three prominently used phase-field models (AT2, AT1, and PF-CZM). We demonstrate the accuracy and computational efficiency of the proposed method by simulating various thermomechanical fracture problems and comparing the results with the nonadaptive phase-field method that adopts a priori nonadaptively refined meshes. We consider different types of thermal and mechanical loading, including thermal shock, to evaluate the proposed approach comprehensively. Our results show that the proposed ML-AMR phase-field method reduces computation time by 78%–99% while accurately capturing the crack path, peak load, and total strain energy.

Topology optimization is an appealing technique for optimal layout of active controllers of structures. However, the existing methods are mainly restricted to deterministic excitations, and the optimal control law involved is determined by use of the classical optimal control (COC) method, in which the sensitivities of the gain matrix with respect to the design variables need to be determined by solving the Riccati sensitivity equation numerically. In this study, a reliability-based topology optimization framework is proposed for optimal layout of active controllers of structures under nonstationary random excitations. The optimization problem is formulated as the minimization of the failure probability of the structure subjected to a specified maximum number of controllers. To avoid solving the Riccati equation, an explicit optimal control (EOC) method is first employed to derive the closed-form optimal control law in terms of the position parameters of controllers. The statistical moments of the optimal control forces and structural responses under random excitations are then obtained explicitly by the operation rules of moments, and the first-passage dynamic reliability of the structure can be formulated using the level-crossing theory. On this basis, the sensitivities of the structural failure probability with respect to the position parameters of controllers can be derived analytically by the direct differential method. Finally, the explicit formulations of the response statistics and the relevant sensitivities are incorporated into a gradient-based method of moving asymptotes (MMA) for topology optimization of the layout of controllers in conjunction with the solid isotropic material with penalization (SIMP) technique. Two numerical examples are presented to demonstrate the feasibility of the proposed topology optimization framework.

Abstract

This article is about a modification of Verlet’s time integration method. First, a one-step version of the basic scheme is described. Subsequently, a diagonal matrix is introduced in the scheme to improve the behavior of Verlet’s method with respect to period elongation. The generic coefficient of this diagonal matrix is defined by referring to the frequency which locally dominates the structural dynamics of the correlated unknown. Since the computation of these coefficients is algorithmic, the method presented does not involve the adjustment of any parameter. Furthermore, the presented modification does not alter the excellent amplitude decay and stability characteristics of the original method. As a result, a second order one-step explicit time integration scheme with desirable accuracy and stability properties is obtained. Several numerical examples for nonlinear problems are conducted to show the ability of the presented method to reduce unwanted period distortion.

Practical Applications

Computational algorithms can automate repetitive design tasks, saving designers time and effort. In this sense, these computational tools provide designers with detailed data insights that can guide decision-making processes. Once implemented, algorithms become effective and useful tools for increasing productivity and creating more robust designs. However, the reliability of the results is a prerequisite for the success of these approaches. In the context of the dynamic behavior of structures, the present work improves a preexisting computational tool to reproduce the motion of the system under study. Practical engineering applications for linear and nonlinear dynamic analysis can then be addressed by introducing data rigor into the design. Starting from appropriate mathematical models for the analyzed structures, the presented algorithm provides an accurate description of the resulting displacements and stresses. All this through a calculation effort comparable to that of the previous method. As demonstrated by the tests carried out, the simulation for the control of suspension systems as well as the seismic response to earthquake excitation on buildings can represent applicative implications in the engineering field.

When excavating the rock foundation of a hydropower station, it will be affected by the phenomenon of unloading and relaxation, which may increase the risk of stability of the dam foundation engineering system. The dam foundation of Baihetan Hydropower is a columnar jointed rock mass (CJRM), which presents strong brittleness and anisotropy compared to traditional dam foundation rocks. Therefore, this type of rock mass is prone to disturbance to the dam body, structure, etc. during excavation, so it is necessary to accurately evaluate the impact of dam foundation excavation. Establishing a rock mass creep models serve as an effective tool for evaluating such stability but often suffer from significant parameter uncertainty. Digital twin technology, a virtual model, is capable of real-time learning from actual monitoring data obtained from the physical entity to enhance the performance of the built-in mechanistic model. In this study, the researchers employ the classical Burgers constitutive equation as the theoretical framework and integrate it with an ensemble smoother with multiple data assimilation (ESMDA) method based on Bayesian principles, along with displacement monitoring data from the Baihetan Dam foundation, to construct a digital twin model. Within this framework, the researchers analyze the uncertainty of rheological parameters at various measurement points in the Baihetan Dam foundation. Subsequently, the most suitable rheological parameters are selected and incorporated into the constitutive model to obtain displacement estimates, which are then compared with on-site monitoring data. The results demonstrate that the proposed method effectively performs probabilistic parameter estimation and model prediction for rheological mechanics. This research integrates data-driven methods with mechanical principles, offering a reliable approach for assessing the uncertainty of unloading rheological parameters and displacement prediction in dam foundations, thereby providing essential support for the evaluation of excavation projects in the CJRM of the Baihetan Dam foundation.