Isogeometric analysis of thin Reissner-Mindlin shells: locking phenomena and B-bar method

in Computational Mechanics (2020), 65(5), 1323-1341

We propose a local type of B-bar formulation, addressing locking in degenerated Reissner–Mindlin shell formulation in the context of isogeometric analysis. Parasitic strain components are projected onto ... [more ▼]

We propose a local type of B-bar formulation, addressing locking in degenerated Reissner–Mindlin shell formulation 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 allows the flexible utilization of basis functions of different orders as the projection bases. The introduced formulation is much cheaper computationally than the classical $$\bar{B}$$B¯ method. We show the numerical consistency of the scheme through numerical examples, moreover they show that the proposed formulation alleviates locking and yields good accuracy even for slenderness ratios of $$10^5$$105, and has the ability to capture deformations of thin shells using relatively coarse meshes. In addition it can be opined that the proposed method is less sensitive to locking with irregular meshes. [less ▲]

Data Centric Engineering and Data-Driven Modelling - Computational Engineering Lab Report 2019

Report (2019)

https://www.cambridge.org/core/journals/data-centric-engineering

Parameter identification problem in bimaterial human skin and sensitivity analysis : Uncertainties in biomechanics of skin

Scientific Conference (2019, December 09)

The proposed paper concerns the prediction of the numerical response of a biomechanical structure submitted to an unknown external loading state. The methodology is based on homogeneous and then ... [more ▼]

The proposed paper concerns the prediction of the numerical response of a biomechanical structure submitted to an unknown external loading state. The methodology is based on homogeneous and then heterogeneous structures such as healthy or pathological cutaneous tissues that can be mechanically tested in vivo under a patchy knowledge of boundary conditions. Experimental data corresponding to the extension of a piece of skin located between two pads with displacement enslavement, represent input data to the numerical model. Data are reaction force on one pad and displacement field between the two pads and all around. The numerical model consists of a representation of the bi-material domain geometry with neo-hookean behaviors. The boundary conditions and loadings of the experimental extension test are imposed. The materials parameters have been identified by inverse method starting from a constrained cost function minimizing the difference between the calculated displacements field and experimental displacements field obtained by digital image correlation and taking into account the reaction force as a constraint. An analysis of the model sensitivity to material parameters is presented. [less ▲]

Fracture mechanism simulation of inhomogeneous anisotropic rocks by extended finite element method

in Theoretical and Applied Fracture Mechanics (2019), 104

The vast majority of rock masses is anisotropic due to factors such as layering, unequal in-situ stresses, joint sets, and discontinuities. Meanwhile, given the frequently asymmetric distribution of pores ... [more ▼]

The vast majority of rock masses is anisotropic due to factors such as layering, unequal in-situ stresses, joint sets, and discontinuities. Meanwhile, given the frequently asymmetric distribution of pores, grain sizes or different mineralogical compounds in different locations, they are often classified as inhomogeneous materials. In such materials, stress intensity factors (SIFs) at the crack tip, which control the initiation of failure, strongly depend on mechanical properties of the material near that area. On the other hand, crack propagation trajectories highly depend on the orthotropic properties of the rock mass. In this study, the SIFs are calculated by means of anisotropic crack tip enrichments and an interaction integral are developed for inhomogeneous materials with the help of the extended finite element method (XFEM). We also use the T-stress within the crack tip fields to develop a new criterion to estimate the crack initiation angles and propagation in rock masses. To verify and validate the proposed approach, the results are compared with experimental test results and those reported in the literature. It is found that the ratio of elastic moduli, shear stiffnesses, and material orientation angles have a significant impact on the SIFs. However, the rate of change in material properties is found to have a moderate effect on these factors and a more pronounced effect on the failure force. The results highlight the potential of the proposed formulation in the estimation of SIFs and crack propagation paths in inhomogeneous anisotropic materials. [less ▲]

Equation-free multiscale modeling of metallic lattices with geometrical and material nonlinearity and variability

Scientific Conference (2019, September 05)

An nonlinear equation-free concurrent multiscale numerical framework, being the generalization of the quasicontinuum method [2] is proposed in this contribution to model 3D metallic lattice structures ... [more ▼]

An nonlinear equation-free concurrent multiscale numerical framework, being the generalization of the quasicontinuum method [2] is proposed in this contribution to model 3D metallic lattice structures. The proposed equation-free multiscale method (EFMM) relies on the use of fully-resolved domains (FRD) in which all of the details of the lattice micro-structure are captured, and of coarse-grained domains (CGD) in which a model reduction is performed by interpolation and summation steps. The particularity of the lattice geometry description is that cross section variations along the lattice struts (that are experimentally observed as a result of the manufacturing process) are explicitly represented by their discretization in several beam finite elements, both in the FRDs and CGDs. The interpolation step of the EFMM refers to a kinematic approximation of the lattice deformation within CGDs based on the movement of a reduced number of material points at the CGD corners. One of the originalities of this work is the consideration of a separate interpolation of each type of degrees of freedom within the CGDs, as a function of the connectivity of the lattice beam nodes (i.e. taking the location of different cross sections into account) and their kinematical pattern. This, together with accounting for plasticity, by the development and implementation of a 3D co-rotational beam finite element [1] with embedded plastic hinges [3], are unprecedented and original contributions. The EFMM is applied to metallic BCC lattices with various sizes and loading conditions. By comparing to direct numerical simulation (DNS), it is shown that both material and geometrical non-linearities can be captured at a fraction of the DNS cost (the computational time is reduced by 97.27% while introducing an error of only 3.76%). [less ▲]

An Implicit boundary approach for viscous compressible high Reynolds flows using hybrid remeshed particle hydrodynamics method

in Journal of Computational Physics (2019), 391

A stochastic Galerkin cell-based smoothed finite element method (SGCS-FEM)

in International Journal of Computational Methods (2019), 17(8),

In this paper, the cell based smoothed finite element method is extended to solve stochastic partial diff erential equations with uncertain input parameters. The spatial field of Young's moduli and the ... [more ▼]

In this paper, the cell based smoothed finite element method is extended to solve stochastic partial diff erential equations with uncertain input parameters. The spatial field of Young's moduli and the corresponding stochastic results are represented by Karhunen-Lo eve expansion and polynomial chaos expansion, respectively. The Young's Modulus of structure is considered to be random for stochastic static as well as free vibration problems. Mathematical expressions and the solution procedure are articulated in detail to evaluate the statistical characteristics of responses in terms of static displacements and free vibration frequencies. The feasibility and eff ectiveness of the proposed SGCS-FEM method in terms of accuracy and lower requirement on the mesh size in the solution domain over that of conventional FEM for stochastic problems are demonstrated by carefully chosen numerical examples. From the numerical study, it is inferred that the proposed framework is computationally less demanding without compromising accuracy. [less ▲]

Structural shape optimization of three dimensional acoustic problems with isogeometric boundary element methods

in Computer Methods in Applied Mechanics and Engineering (2019), 355

The boundary element method (BEM) is a powerful tool in computational acoustics, because the analysis is conducted only on structural surfaces, compared to the finite element method (FEM) which resorts to ... [more ▼]

The boundary element method (BEM) is a powerful tool in computational acoustics, because the analysis is conducted only on structural surfaces, compared to the finite element method (FEM) which resorts to special techniques to truncate infinite domains. The isogeometric boundary element method (IGABEM) is a recent progress in the category of boundary element approaches, which is inspired by the concept of isogeometric analysis (IGA) and employs the spline functions of CAD as basis functions to discretize unknown physical fields. As a boundary representation approach, IGABEM is naturally compatible with CAD and thus can directly perform numerical analysis on CAD models, avoiding the cumbersome meshing procedure in conventional FEM/BEM and eliminating the difficulty of volume parameterization in isogeometric finite element methods. The advantage of tight integration of CAD and numerical analysis in IGABEM renders it particularly attractive in the application of structural shape optimization because (1) the geometry and the analysis can be interacted, (2) remeshing with shape morphing can be avoided, and (3) an optimized solution returns a CAD geometry directly without postprocessing steps. In the present paper, we apply the IGABEM to structural shape optimization of three dimensional exterior acoustic problems, fully exploiting the strength of IGABEM in addressing infinite domain problems and integrating CAD and numerical analysis. We employ the Burton–Miller formulation to overcome fictitious frequency problems, in which hyper-singular integrals are evaluated explicitly. The gradient-based optimizer is adopted and shape sensitivity analysis is conducted with implicit differentiation methods. The design variables are set to be the positions of control points which directly determine the shape of structures. Finally, numerical examples are provided to verify the algorithm. [less ▲]

Multiscale fracture: a natural connection between reduced order models and homogenisation

Scientific Conference (2019, May 13)

ADVANCES IN GEOMETRY INDEPENDENT APPROXIMATIONS

Scientific Conference (2019, April 11)

We present recent advances in geometry independent field approximations. The GIFT approach is a generalisation of isogeometric analysis where the approximation used to describe the field variables no ... [more ▼]

We present recent advances in geometry independent field approximations. The GIFT approach is a generalisation of isogeometric analysis where the approximation used to describe the field variables no-longer has to be identical to the approximation used to describe the geometry of the domain. As such, the geometry can be described using usual CAD representations, e.g. NURBS, which are the most common in the CAD area, whilst local refinement and meshes approximations can be used to describe the field variables, enabling local adaptivity. We show in which cases the approach passes the patch test and present applications to various mechanics, fracture and multi-physics problems. [less ▲]