journal article
LitStream Collection
Home
Seoane, M.; Ledger, P.D.; Gil, A.J.; Mallett, M.
doi: 10.1002/nme.6088pmid: N/A
Transient magnetic fields are generated by the gradient coils in an magnetic resonance imaging (MRI) scanner and induce eddy currents in their conducting components, which lead to vibrations, imaging artefacts, noise, and the dissipation of heat. Heat dissipation can boil off the helium used to cool the super conducting magnets and, if left unchecked, will lead to a magnet quench. Understanding the mechanisms involved in the generation of these vibrations, and the heat being deposited in the cryostat, are key for a successful MRI scanner design. This requires the solution of a coupled physics magneto‐mechanical problem, which will be addressed in this work. A novel computational methodology is proposed for the accurate simulation of the magneto‐mechanical problem using a Lagrangian approach, which, with a particular choice of linearisation, leads to a staggered scheme. This is discretised by high‐order finite elements leading to accurate solutions. We demonstrate the success of our scheme by applying it to realistic MRI scanner configurations.
doi: 10.1002/nme.6089pmid: N/A
In the present paper, structure‐preserving numerical methods for finite strain thermoelastodynamics are proposed. The underlying variational formulation is based on the general equation for nonequilibrium reversible‐irreversible coupling (GENERIC) formalism and makes possible the free choice of the thermodynamic state variable. The notion “GENERIC consistent space discretization” is introduced, which facilitates the design of Energy‐Momentum‐Entropy (EME) consistent schemes. In particular, three alternative EME schemes result from the present approach. These schemes are directly linked to the respective choice of the thermodynamic variable. Numerical examples confirm the structure‐preserving properties of the newly developed EME schemes, which exhibit superior numerical stability.
doi: 10.1002/nme.6090pmid: N/A
An improved eight‐noded isoparametric quadratic plate bending element based on refined higher‐order zigzag theory (RHZT) has been developed in the present study to determine the interlaminar stresses of multilayered composite laminates. The C0 continuous element has been formulated by considering warping function in the displacement field based on the RHZT. Shear locking phenomenon is avoided by considering substitute shear strain field. The continuity of transverse shear stresses cannot be ensured by the proposed zigzag formulation directly, and hence, the continuity conditions of transverse shear stresses have been established by using the three‐dimensional (3D) stress equilibrium equations in the present study. The transverse shear stresses are computed in a simplified manner using the differential equations of stress equilibrium. A finite element code is developed by using MATLAB software package. The performance of the present finite element model is validated by comparing the results with 3D elasticity solutions. The superiority of the proposed element in view of computational efficiency, simplicity, and accuracy has been examined by comparing the present solutions with those available in published literature using other elements.
Lins, Rafael; Proença, Sergio Persival; Duarte, C. Armando
doi: 10.1002/nme.6091pmid: N/A
This paper presents a new stress recovery technique for the generalized/extended finite element method (G/XFEM) and for the stable generalized FEM (SGFEM). The recovery procedure is based on a locally weighted L2 projection of raw stresses over element patches; the set of elements sharing a node. Such projection leads to a block‐diagonal system of equations for the recovered stresses. The recovery procedure can be used with GFEM and SGFEM approximations based on any choice of elements and enrichment functions. Here, the focus is on low‐order 2D approximations for linear elastic fracture problems. A procedure for computing recovered stresses at re‐entrant corners of any internal angle is also presented. The proposed stress recovery technique is used to define a Zienkiewicz‐Zhu (ZZ) a posteriori error estimator for the G/XFEM and the SGFEM. The accuracy, computational cost, and convergence rate of recovered stresses together with the quality of the ZZ estimator, including its effectivity index, are demonstrated in problems with smooth and singular solutions.
Wang, Lei; Liu, Yisi; Yang, Yaowen
doi: 10.1002/nme.6092pmid: N/A
A nonprobabilistic reliability‐based topology optimization (NRBTO) method for truss structures with interval uncertainties (or unknown‐but‐bounded uncertainties) is proposed in this paper. The cross‐sectional areas of levers are defined as design variables, while the material properties and external loads are regard as interval parameters. A modified perturbation method is applied to calculate structural response bounds, which are the prerequisite to obtain structural reliability. A deviation distance between the current limit state plane and the objective limit state plane, of which the expression is explicit, is defined as the nonprobabilistic reliability index, which serves as a constraint function in the optimization model. Compared with the deterministic topology optimization problem, the proposed NRBTO formulation is still a single‐loop optimization problem, as the reliability index is explicit. The sensitivity results are obtained from an analytical approach as well as a direct difference method. Eventually, the NRBTO problem is solved by a sequential quadratic programming method. Two numerical examples are used to testify the validity and effectiveness of the proposed method. The results show significant effects of uncertainties to the topology configuration of truss structures.
Showing 1 to 6 of 6 Articles