Computational analysis of cold-formed steel columns with initial imperfections

Cold-formed steel (CFS) structures experience very complicated buckling and post-buckling performance. The presence of any kind of uncertainties complicates the calculation of such structures. Thin-walled CFS members are known to be particularly vulnerable to the influence of initial geometric imperfections. These imperfections may be the outcome of the manufacturing process, shipping and storage or the construction process. The article provides the results of nonlinear buckling analyses of CFS C-shaped compressed columns and evaluates the influence of imperfections on the load-bearing capacity of the tested members

Interpolation of Microscale Stress and Strain Fields Based on Mechanical Models

In this short contribution we introduce a new procedure to recover the stress and strain fields for particle systems by mechanical models. Numerical tests for simple loading conditions have shown an excellent match between the estimated values and the reference values. The estimated stress field is also consistent with the so called Quasicontinuum stress field, which suggests its potential application for scale bridging techniques. The estimated stress fields for complicated loading conditions such as defect and indentation are also demonstrate

Stochastic virtual element methods for uncertainty propagation of stochastic linear elasticity

This paper presents stochastic virtual element methods for propagating uncertainty in linear elastic stochastic problems. We first derive stochastic virtual element equations for 2D and 3D linear elastic problems that may involve uncertainties in material properties, external forces, etc. A stochastic virtual element space that couples the deterministic virtual element space and the stochastic space is constructed for this purpose and used to approximate the unknown stochastic solution. Two numerical frameworks are then developed to solve the derived stochastic virtual element equations, including a Polynomial Chaos approximation based approach and a weakly intrusive approximation based approach. In the PC based framework, the stochastic solution is approximated using the Polynomial Chaos basis and solved via an augmented deterministic virtual element equation that is generated by applying the stochastic Galerkin procedure to the original stochastic virtual element equation. In the weakly intrusive approximation based framework, the stochastic solution is approximated by a summation of a set of products of random variables and deterministic vectors, where the deterministic vectors are solved via converting the original stochastic problem to deterministic virtual element equations by the stochastic Galerkin approach, and the random variables are solved via converting the original stochastic problem to one-dimensional stochastic algebraic equations by the classical Galerkin procedure. This method avoids the curse of dimensionality of high-dimensional stochastic problems successfully since all random inputs are embedded into one-dimensional stochastic algebraic equations whose computational effort weakly depends on the stochastic dimension. Numerical results on 2D and 3D problems with low- and high-dimensional random inputs demonstrate the good performance of the proposed methods

A fully implicit and thermodynamically consistent finite element framework for bone remodeling simulations

This work addresses the thermodynamically consistent formulation of bone remodeling as a fully implicit finite element material model. To this end, bone remodeling is described in the framework of thermodynamics for open systems resulting in a thermodynamically consistent constitutive law. In close analogy to elastoplastic material modeling, the constitutive equations are implicitly integrated in time and incorporated into a finite element weak form. A consistent linearization scheme is provided for the subsequent incremental non-linear boundary value problem, resulting in a computationally efficient description of bone remodeling. The presented model is suitable for implementation in any standard finite element framework with quadratic or higher-order element types. Two numerical examples in three dimensions are shown as proof of the efficiency of the proposed method

Stochastic virtual element methods for uncertainty propagation of stochastic linear elasticity

This paper presents stochastic virtual element methods for propagating uncertainty in linear elastic stochastic problems. We first derive stochastic virtual element equations for 2D and 3D linear elastic problems that may involve uncertainties in material properties, external forces, boundary conditions, etc. A stochastic virtual element space that couples the deterministic virtual element space and the stochastic space is constructed for this purpose and used to approximate the unknown stochastic solution. Two numerical frameworks are then developed to solve the derived stochastic virtual element equations, including a Polynomial Chaos approximation based approach and a weakly intrusive approximation based approach. In the Polynomial Chaos based framework, the stochastic solution is approximated using the Polynomial Chaos basis and solved via an augmented deterministic virtual element equation that is generated by applying the stochastic Galerkin procedure to the original stochastic virtual element equation. In the weakly intrusive approximation based framework, the stochastic solution is approximated by a summation of a set of products of random variables and deterministic vectors, where the deterministic vectors are solved via converting the original stochastic problem to deterministic virtual element equations by the stochastic Galerkin approach, and the random variables are solved via converting the original stochastic problem to one-dimensional stochastic algebraic equations by the classical Galerkin procedure. This method avoids the curse of dimensionality in high-dimensional stochastic problems successfully since all random inputs are embedded into one-dimensional stochastic algebraic equations whose computational effort weakly depends on the stochastic dimension. Numerical results on 2D and 3D problems with low- and high-dimensional random inputs demonstrate the good performance of the proposed methods

A nonlinear stochastic finite element method for solving elastoplastic problems with uncertainties

This article presents an efficient nonlinear stochastic finite element method to solve stochastic elastoplastic problems. Similar to deterministic elastoplastic problems, we describe history-dependent stochastic elastoplastic behavior utilizing a series of (pseudo) time steps and go further to solve the corresponding stochastic solutions. For each time step, the original stochastic elastoplastic problem is considered as a time-independent nonlinear stochastic problem with initial values given by stochastic displacements, stochastic strains, and internal variables of the previous time step. To solve the stochastic solution at each time step, the corresponding nonlinear stochastic problem is transformed into a set of linearized stochastic finite element equations by means of finite element discretization and a stochastic Newton linearization, while the stochastic solution at each time step is approximated by a sum of the products of random variables and deterministic vectors. Each couple of the random variable and the deterministic vector is also used to approximate the stochastic solution of the corresponding linearized stochastic finite element equation that can be solved via a weakly intrusive method. In this method, the deterministic vector is computed by solving deterministic linear finite element equations, and corresponding random variables are solved by a non-intrusive method. Further, the proposed method avoids the curse of dimensionality successfully since its computational effort does not increase dramatically as the stochastic dimensionality increases. Four numerical cases are used to demonstrate the good performance of the proposed method

Micro-feature-motivated numerical analysis of the coupled bio-chemo-hydro-mechanical behaviour in MICP

A coupled bio-chemo-hydro-mechanical model (BCHM) is developed to investigate the permeability reduction and stiffness improvement in soil by microbially induced calcite precipitation (MICP). Specifically, in our model based on the geometric method a link between the micro- and macroscopic features is generated. This allows the model to capture the macroscopic material property changes caused by variations in the microstructure during MICP. The developed model was calibrated and validated with the experimental data from different literature sources. Besides, the model was applied in a scenario simulation to predict the hydro-mechanical response of MICP-soil under continuous biochemical, hydraulic and mechanical treatments. Our modelling study indicates that for a reasonable prediction of the permeability reduction and stiffness improvement by MICP in both space and time, the coupled BCHM processes and the influences from the microstructural aspects should be considered. Due to its capability to capture the dynamic BCHM interactions in flexible settings, this model could potentially be adopted as a designing tool for real MICP applications. © 2022, The Author(s)

Computing Arlequin coupling coefficient for concurrent FE-MD approaches

Arlequin coupling coefficient is essential for concurrent FE-MD models with overlapping domains, but the calculation of its value is quite difficult when the geometry of the coupling region is complicated. In this work, we introduce a general procedure for the preprocessing of a concurrent FE-MD model, given that the mesh and atoms have already been created. The procedure is independent of the geometry of the coupling region and can be used for both 2D and 3D problems. The procedure includes steps of determining the relative positions of atoms inside the FE elements in the coupling region, as well as computing the Arlequin coupling coefficient for an arbitrary point inside the coupling region or on its boundary. Two approaches are provided for determining the coefficient: the direct approach and the temperature approach

Efficient model-correction-based reliability analysis of uncertain dynamical systems

The scope of this paper is to apply a model-correction-based strategy for efficient reliability analysis of uncertain dynamical systems based on a low-fidelity (LF) model whose outcomes are corrected in a probabilistic sense to represent the more realistic outcomes of a high-fidelity (HF) model. In the model-correction approach utilized, the LF model is calibrated to the HF model close to the so-called most probable point in standard normal space, which allows a more realistic assessment of the considered complex dynamical system. Since only few expensive limit state function evaluations of the HF model are required, an efficient reliability analysis is enabled. In an application example, the LF model describes an existing single-span railway bridge modelled as simply supported Euler–Bernoulli beam subjected to moving single forces representing the axle loads of a moving train. The HF modelling approach accounts for the bridge–train interaction by modelling the passing train as mass-spring-damper system, however increasing the computational effort of the limit state function evaluations. Failure probabilities evaluated with the model-correction approach are contrasted and discussed with failure probabilities of the sophisticated bridge–train interaction model evaluated with the first-order reliability method (FORM). It is demonstrated that the efficiency of the method depends on the correlation between the LF and the HF model. A comparison of the results of FORM and the model-correction-based approach shows that the latter provides reliable failure probability prediction of the HF model while leading to a significant reduction in computational effort

Semi-reduced order stochastic finite element methods for solving contact problems with uncertainties

This paper develops two-step methods for solving contact problems with uncertainties. In the first step, we propose stochastic Lagrangian multiplier/penalty methods to compute a set of reduced basis. In the stochastic Lagrangian multiplier method, the stochastic solution is represented as a sum of products of a set of random variables and deterministic vectors. In the stochastic penalty method, the problem is divided into the solutions of non-contact and possible contact nodes, which are represented as sums of the products of two different sets of random variables and deterministic vectors, respectively. The original problems are then transformed into deterministic finite element equations and one-dimensional (corresponding to stochastic Lagrangian multiplier method)/two-dimensional (corresponding to stochastic penalty method) stochastic algebraic equations. The deterministic finite element equations are solved by existing numerical techniques, and the one-/two-dimensional stochastic algebraic equations are solved by a sampling method. Since the computational cost for solving stochastic algebraic equations does not increase dramatically as the stochastic dimension increases, the proposed methods avoid the curse of dimensionality in high-dimensional problems. Based on the reduced basis, we propose semi-reduced order Lagrangian multiplier/penalty equations with two components in the second step. One component is a reduced order equation obtained by smooth solutions of the reduced basis and the other is the full order equation for the nonsmooth solutions. A significant amount of computational cost is saved since the sizes of the semi-reduced order equations are usually small. Numerical examples of up to 100 dimensions demonstrate the good performance of the proposed methods