We exploit level-set topology optimization to find the optimal material distribution for metamaterial-based heat manipulators. The level-set function, geometry, and solution field are parameterized ...using the Non-Uniform Rational B-Spline (NURBS) basis functions to take advantage of easy control of smoothness and continuity. In addition, NURBS approximations can produce conic geometries exactly and provide higher efficiency for higher-order elements. The values of the level-set function at the control points (called expansion coefficients) are utilized as design variables. For optimization, we use an advanced mathematical programming technique, Sequential Quadratic Programming. Taking into account a large number of design variables and the small number of constraints associated with our optimization problem, the adjoint method is utilized to calculate the required sensitivities with respect to the design variables. The efficiency and robustness of the proposed method are demonstrated by solving three numerical examples. We have also shown that the current method can handle different geometries and types of objective functions. In addition, regularization techniques such as Tikhonov regularization and volume regularization have been explored to reduce unnecessary complexity and increase the manufacturability of optimized topologies.
We propose a method for simulating linear elastic crack growth through an isogeometric boundary element method directly from a CAD model and without any mesh generation. To capture the stress ...singularity around the crack tip, two methods are compared: (1) a graded knot insertion near crack tip; (2) partition of unity enrichment. A well-established CAD algorithm is adopted to generate smooth crack surfaces as the crack grows. The
M
integral and
J
k
integral methods are used for the extraction of stress intensity factors (SIFs). The obtained SIFs and crack paths are compared with other numerical methods.
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
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
, 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.
This work models spatially uncorrelated (independent) load uncertainty and develops a reduced-order Monte Carlo stochastic isogeometric method to quantify the effect of the load uncertainty on the ...structural response of thin shells and solid structures. The approach is tested on two demonstrative applications of uncertainty, namely, spatially uncorrelated loading, with (1) Scordelis–Lo Roof shell structure, and (2) a 3D wind turbine blade. This work has three novelties. Firstly, the research models spatially uncorrelated (independent) load uncertainties (including both their magnitude and/or direction) using stochastic analysis. Secondly, the paper advances a reduced-order Monte Carlo stochastic isogeometric method to quantify the spatially uncorrelated load uncertainty. It inherits the merits of isogeometric analysis, which enables the precise representation of geometry and alleviates shell shear locking, thereby reducing the model’s uncertainties. Moreover, the method retains the generality and accuracy of classical Monte Carlo simulation (MCS), with significant efficiency gains. The demonstrative results suggest that there is a cost, which is 3% of the time used by the standard MCS. Furthermore, a significant observation is made from the conducted numerical tests. It is noticed that the standard deviation of the output (i.e., displacement) is strongly influenced when the load uncertainty is spatially uncorrelated. Namely, the standard derivation (SD) of the output is roughly 10 times smaller than the SD for correlated load uncertainties. Nonetheless, the expected values remain consistent between the two cases.
This contribution discusses surrogate models that emulate the solution field(s) in the entire simulation domain. The surrogate uses the most characteristic modes of the solution field(s), in ...combination with neural networks to emulate the coefficients of each mode. This type of surrogate is well known to rapidly emulate flow simulations, but rather new for simulations of elastoplastic solids. The surrogate avoids the iterative process of constructing and solving the linearized governing equations of rate-independent elastoplasticity, as necessary for direct numerical simulations or (hyper-)reduced-order-models. Instead, the new plastic variables are computed only once per increment, resulting in substantial time savings. The surrogate uses a recurrent neural network to treat the path dependency of rate-independent elastoplasticity within the neural network itself. Because only a few of these surrogates have been developed for elastoplastic simulations, their potential and limitations are not yet well studied. The aim of this contribution is to shed more light on their numerical capabilities in the context of elastoplasticity. Although more widely applicable, the investigation focuses on a representative volume element, because these surrogates have the ability to both emulate the macroscale stress-deformation relation (which drives the multiscale simulation), as well as to recover all microstructural quantities within each representative volume element.
AbstractIn this paper, we establish a coupled damage-plastic constitutive model in the scheme of small deformation assumption, based on a continuum damage mechanics model proposed by Lemaitre, for ...the thin-walled circular steel tubes widely used in space structures. First, a new damage evolution law is developed for steel tubes. Then the isotropic damage-plastic constitutive model is created within the thermodynamics framework. In addition, the numerical integration algorithm for the proposed model is formulated based on the well-established operator split methodology and is implemented into ANSYS through the user-defined material subroutines. The uniaxial tension test and the spatial hysteresis experiment for thin-walled circular steel tubes are performed, which serves as calibration conditions for the new proposition. The model parameters are determined by the inverse optimization method and the least squares fitting method. Numerical results obtained from the proposed and Lemaitre model are compared with experimental data obtained by spatial hysteresis, and the predictive ability of both models is discussed in terms of the force-displacement hysteretic curves, the initiation and propagation of fracture, and the evolution of the damage variable. It is illustrated that the established model presents a good agreement with experimental observation. Furthermore, it performs a better prediction compared to Lemaitre’s model. Lemaitre’s model is able to predict the correct location for fracture onset but fails to capture the potential path of fracture propagation and the displacement at the fracture.
The unique mechanical, electrical, thermal, chemical and optical properties of carbon based nanomaterials (CBNs) like: Fullerenes, Graphene, Carbon nanotubes, and their derivatives made them widely ...used materials for various applications including biomedicine. Few recent applications of the CBNs in biomedicine include: cancer therapy, targeted drug delivery, bio-sensing, cell and tissue imaging and regenerative medicine. However, functionalization renders the toxicity of CBNs and makes them soluble in several solvents including water, which is required for biomedical applications. Hence, this review represents the complete study of development in nanomaterials of carbon for biomedical uses. Especially, CBNs as the vehicles for delivering the drug in carbon nanomaterials is described in particular. The computational modeling approaches of various CBNs are also addressed. Furthermore, prospectus, issues and possible challenges of this rapidly developing field are highlighted.
Linear smoothed extended finite element method Surendran, M.; Natarajan, Sundararajan; Bordas, Stéphane P. A. ...
International journal for numerical methods in engineering,
21 December 2017, 2017-12-21, 20171221, Letnik:
112, Številka:
12
Journal Article
Recenzirano
Odprti dostop
Summary
The extended finite element method was introduced in 1999 to treat problems involving discontinuities with no or minimal remeshing through appropriate enrichment functions. This enables ...elements to be split by a discontinuity, strong or weak, and hence requires the integration of discontinuous functions or functions with discontinuous derivatives over elementary volumes. A variety of approaches have been proposed to facilitate these special types of numerical integration, which have been shown to have a large impact on the accuracy and the convergence of the numerical solution. The smoothed extended finite element method (XFEM), for example, makes numerical integration elegant and simple by transforming volume integrals into surface integrals. However, it was reported in the literature that the strain smoothing is inaccurate when non‐polynomial functions are in the basis. In this paper, we investigate the benefits of a recently developed Linear smoothing procedure which provides better approximation to higher‐order polynomial fields in the basis. Some benchmark problems in the context of linear elastic fracture mechanics are solved and the results are compared with existing approaches. We observe that the stress intensity factors computed through the proposed linear smoothed XFEM is more accurate than that obtained through smoothed XFEM.
Linear smoothed polygonal and polyhedral finite elements Francis, Amrita; Ortiz‐Bernardin, Alejandro; Bordas, Stéphane PA ...
International journal for numerical methods in engineering,
2 March 2017, Letnik:
109, Številka:
9
Journal Article
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