Deep neural network with high-order neuron for the prediction of foamed concrete strength

in Computer-Aided Civil and Infrastructure Engineering (2018)

The article presents a deep neural network model for the prediction of the compressive strength of foamed concrete. A new, high-order neuron was developed for the deep neural network model to improve the ... [more ▼]

The article presents a deep neural network model for the prediction of the compressive strength of foamed concrete. A new, high-order neuron was developed for the deep neural network model to improve the performance of the model. Moreover, the cross-entropy cost function and rectified linear unit activation function were employed to enhance the performance of the model. The present model was then applied to predict the compressive strength of foamed concrete through a given data set, and the obtained results were compared with other machine learning methods including conventional artificial neural network (C-ANN) and second-order artificial neural network (SO-ANN). To further validate the proposed model, a new data set from the laboratory and a given data set of high-performance concrete were used to obtain a higher degree of confidence in the prediction. It is shown that the proposed model obtained a better prediction, compared to other methods. In contrast to C-ANN and SO-ANN, the proposed model can genuinely improve its performance when training a deep neural network model with multiple hidden layers. A sensitivity analysis was conducted to investigate the effects of the input variables on the compressive strength. The results indicated that the compressive strength of foamed concrete is greatly affected by density, followed by the water-to-cement and sand-to-cement ratios. By providing a reliable prediction tool, the proposed model can aid researchers and engineers in mixture design optimization of foamed concrete. [less ▲]

A parallel and efficient multi-split XFEM for 3-D analysis of heterogeneous materials

in Computer Methods in Applied Mechanics and Engineering (2018)

We propose a parallel and computationally efficient multi-split XFEM approach for 3-D analysis of heterogeneous materials. In this approach, multiple discontinuities (pores and reinforcement particles ... [more ▼]

We propose a parallel and computationally efficient multi-split XFEM approach for 3-D analysis of heterogeneous materials. In this approach, multiple discontinuities (pores and reinforcement particles) may intersect any given element (we call those elements multi-split elements). These discontinuities are modeled by imposing additional degrees of freedom at the nodes. The main advantage of the proposed scheme is that the mesh size remains independent of the relative distance among the heterogeneities/discontinuities. The pores and reinforcement particles are assumed to be spherical. The simulations are performed for uniform and non-uniform heterogeneity distribution. The Young’s modulus of the heterogeneous material is evaluated for different amount of pores and reinforcement particles. To demonstrate the computational efficiency of the multi-split XFEM, elastic damage analysis is performed for the unit cell with 5% pores and 5% reinforcement particles under uniaxial tensile loading. These simulations show that the Young’s modulus decreases linearly with the increase in the volume fraction of the pores and increases linearly with the increase in volume fraction of reinforcement particles. The multi-split XFEM is found to be at least 1.8 times computationally efficient than standard XFEM and at least 6.7 times computationally efficient than FEM. [less ▲]

Weakening the tight coupling between geometry and simulation in isogeometric analysis: from sub- and super- geometric analysis to Geometry Independent Field approximaTion (GIFT)

in International Journal for Numerical Methods in Engineering (2018)

This paper presents an approach to generalize the concept of isogeometric analysis (IGA) by allowing different spaces for parameterization of the computational domain and for approximation of the solution ... [more ▼]

This paper presents an approach to generalize the concept of isogeometric analysis (IGA) by allowing different spaces for parameterization of the computational domain and for approximation of the solution field. The method inherits the main advantage of isogeometric analysis, i.e. preserves the original, exact CAD geometry (for example, given by NURBS), but allows pairing it with an approximation space which is more suitable/flexible for analysis, for example, T-splines, LR-splines, (truncated) hierarchical B-splines, and PHT-splines. This generalization offers the advantage of adaptive local refinement without the need to re-parameterize the domain, and therefore without weakening the link with the CAD model. We demonstrate the use of the method with different choices of the geometry and field splines, and show that, despite the failure of the standard patch test, the optimum convergence rate is achieved for non-nested spaces. [less ▲]

Adaptive Isogeometric analysis for plate vibrations: An efficient approach of local refinement based on hierarchical a posteriori error estimation

in Computer Methods in Applied Mechanics and Engineering (2018), 342

This paper presents a novel methodology of local adaptivity for the frequency-domain analysis of the vibrations of Reissner–Mindlin plates. The adaptive discretization is based on the recently developed ... [more ▼]

This paper presents a novel methodology of local adaptivity for the frequency-domain analysis of the vibrations of Reissner–Mindlin plates. The adaptive discretization is based on the recently developed Geometry Independent Field approximaTion (GIFT) framework, which may be seen as a generalization of the Iso-Geometric Analysis (IGA).Within the GIFT framework, we describe the geometry of the structure exactly with NURBS (Non-Uniform Rational B-Splines), whilst independently employing Polynomial splines over Hierarchical T-meshes (PHT)-splines to represent the solution field. The proposed strategy of local adaptivity, wherein a posteriori error estimators are computed based on inexpensive hierarchical h-refinement, aims to control the discretization error within a frequency band. The approach sweeps from lower to higher frequencies, refining the mesh appropriately so that each of the free vibration mode within the targeted frequency band is sufficiently resolved. Through several numerical examples, we show that the GIFT framework is a powerful and versatile tool to perform local adaptivity in structural dynamics. We also show that the proposed adaptive local h-refinement scheme allows us to achieve significantly faster convergence rates than a uniform h-refinement. [less ▲]

Calculating the Malliavin derivative of some stochastic mechanics problems

in PLoS ONE (2017), 12(12), 0189994

The Malliavin calculus is an extension of the classical calculus of variations from deterministic functions to stochastic processes. In this paper we aim to show in a practical and didactic way how to ... [more ▼]

The Malliavin calculus is an extension of the classical calculus of variations from deterministic functions to stochastic processes. In this paper we aim to show in a practical and didactic way how to calculate the Malliavin derivative, the derivative of the expectation of a quantity of interest of a model with respect to its underlying stochastic parameters, for four problems found in mechanics. The non-intrusive approach uses the Malliavin Weight Sampling (MWS) method in conjunction with a standard Monte Carlo method. The models are expressed as ODEs or PDEs and discretised using the finite difference or finite element methods. Specifically, we consider stochastic extensions of; a 1D Kelvin-Voigt viscoelastic model discretised with finite differences, a 1D linear elastic bar, a hyperelastic bar undergoing buckling, and incompressible Navier-Stokes flow around a cylinder, all discretised with finite elements. A further contribution of this paper is an extension of the MWS method to the more difficult case of non-Gaussian random variables and the calculation of second-order derivatives. We provide open-source code for the numerical examples in this paper. [less ▲]

Isogeometric analysis of thin Reissner-Mindlin plates and shells: Locking phenomena and generalized local B-bar method

E-print/Working paper (2017)

We propose a generalized local $\bar{B}$ framework, addressing locking in degenerated Reissner-Mindlin plate and shell formulations in the context of isogeometric analysis. Parasitic strain components are ... [more ▼]

We propose a generalized local $\bar{B}$ framework, addressing locking in degenerated Reissner-Mindlin plate and shell formulations in the context of isogeometric analysis. Parasitic strain components are projected onto the physical space locally, i.e. at the element level, using a least-squares approach. The formulation is general and allows the flexible utilization of basis functions of different order as the projection bases. The present formulation is much cheaper computationally than the global $\bar{B}$ method. Through numerical examples, we show the consistency of the scheme, although the method is not Hu-Washizu variationally consistent. The numerical examples show that the proposed formulation alleviates locking and yields good accuracy for various thicknesses, even for slenderness ratios of $1 \times 10^5$, and has the ability to capture deformations of thin shells using relatively coarse meshes. From the detailed numerical study, it can be opined that the proposed method is less sensitive to locking and mesh distortion. [less ▲]

Discretisation and Model Selection for Interface Problems in Mechanics

in International Journal of Computational Methods (2017, August 04)

Error-controlled computational fracture mechanics

Scientific Conference (2017, July 12)

Towards a seamless Integration of CAD and Simulation: CISM Course 2017

Learning material (2017)

Isogeometric analysis relies on the use of the same basis functions as employed in Computer Aided Design (CAD). This offers the possibility to facilitate design and optimisation. The previous course ... [more ▼]

Isogeometric analysis relies on the use of the same basis functions as employed in Computer Aided Design (CAD). This offers the possibility to facilitate design and optimisation. The previous course “Isogeometric methods for numerical simulation” held in 2013 had the aim to give an introduction to isogeometric analysis, its advantages, drawbacks and to the range of its applications. The aim of the proposed new course will be different. The focus will be more on the connection of simulation to CAD systems and how CAD data can be used directly for simulation, leading to a seamless integration. An overview of recent advances and applications will be also presented. The course will start with an introduction to NURBS and their use in describing geometry and in simulation. This will be followed by lectures from a CAD vendor describing the current state of development. Currently available connections to simulation software will also be discussed. Next the use of NURBS for 3D structural analysis, structural optimisation and damage tolerance assessment will be presented, including such advanced topics as the treatment of discontinuities and real-time solvers. It will also be discussed when it might be advantageous to decouple the boundary discretisation from the field variable discretisation, in particular in shape optimisation. Isogeometric methods for the analysis of beam and shell structures, including shape optimisation and fluid structure interaction, will be presented. Lectures on the mathematical and algorithmic foundations of analysis-suitable geometry will follow. This includes an introduction to T-splines and multilevel spline schemes such as hierarchical B- splines. Common analysis-suitable spline algorithms will be presented in the context of Bézier extraction and projection as well as its application as a foundation for integrated engineering design and analysis. An important aspect of analysis-suitable geometry is the ability to locally adapt the smooth spline basis. Several common refinement algorithms will be reviewed as well as their application in several demanding areas of application. The emerging area of weak geometry will be introduced as well as its application to the rapid construction of complex structural assemblies. With the rapid development of isogeometric analysis in recent years, there is an urgent need for volumetric parameterization such as volumetric T-spline model construction. Several volumetric T- spline modeling techniques, that were developed in recent years will be presented. They include converting any quad/ hex meshes to standard and rational T-splines, polycube-based parametric mapping, feature preservation using eigenfunctions, Boolean operations and skeletons, truncated hierarchical Catmull-Clark subdivision, weighted T-splines, conformal T-spline modeling, as well as incorporating T-splines into commercial CAD and FEA software, will be presented. The target audience will be engineers, interested in simulation, software developers and researchers. [less ▲]

Modelling hydraulic fractures in porous media using flow cohesive interface elements

in Engineering Geology (2017), 225