International Journal for Numerical Methods in Engineering

Boucher, Ray; Wells, Martin

doi: 10.1002/nme.4660pmid: N/A

Rangarajan, Ramsharan; Lew, Adrián J.

doi: 10.1002/nme.4624pmid: N/A

We introduce a new method to triangulate planar, curved domains that transforms a specific collection of triangles in a background mesh to conform to the boundary. In the process, no new vertices are introduced, and connectivities of triangles are left unaltered. The method relies on a novel way of parameterizing an immersed boundary over a collection of nearby edges with its closest point projection. To guarantee its robustness, we require that the domain be C2‐regular, the background mesh be sufficiently refined near the boundary, and that specific angles in triangles near the boundary be strictly acute. The method can render both straight‐edged and curvilinear triangulations for the immersed domain. The latter includes curved triangles that conform exactly to the immersed boundary, and ones constructed with isoparametric mappings to interpolate the boundary at select points. High‐order finite elements constructed over these curved triangles achieve optimal accuracy, which has customarily proven difficult in numerical schemes that adopt nonconforming meshes.

Kim, Suh In; Kim, Yoon Young

doi: 10.1002/nme.4635pmid: N/A

In spite of increasing interest in gradient‐based topology optimization of linkage mechanisms, it is still difficult to solve practical, realistic problems. Besides the apparent difficulty resulting from high nonlinearity, the optimization problem faces other major difficulties: difficulty to satisfy the discrete DOF condition with continuous design variables and lack of intrinsic mechanisms to generate distinct black‐and‐white layouts. To deal with the DOF issue, we propose a new formulation, which maximizes a single objective function, the energy transmittance efficiency. It is shown that the efficiency function maximization handles DOF redundancy and deficiency simultaneously. To obtain distinct linkage layouts, a common practice is to introduce an artificial mass constraint and/or to remove unnecessary links during optimization. However, we do not use any artificial mass constraint but post‐process the optimized result to obtain the final layout by a special post‐processing algorithm. In this study, the linkage design model consists of nonlinear ground bars and zero‐length springs. The springs are used to fix bar‐connecting nodes to the ground, generating pinned joints. After verifying the effectiveness of the proposed approach for four‐bar linkage synthesis, we synthesize an automobile steering mechanism satisfying the Ackermann condition. The steering mechanism problem is solved here for the first time. Copyright © 2014 John Wiley & Sons, Ltd.

Grange, S.

doi: 10.1002/nme.4638pmid: N/A

An integration procedure designed to satisfy plane stress conditions for any constitutive law initially described in 3D and based on classical plasticity theory is presented herein. This method relies on multi‐surface plasticity, which allows associating in series various mechanisms. Three mechanisms have ultimately been used and added to the first one to satisfy the plane stress conditions. They are chosen to generate a plastic flow in the 3 out‐of‐plane directions, whose stresses must be canceled (σ33,σ13, and σ23). The advantage of this method lies in its ease of use for every plastic constitutive law (in the general case of the non‐associated flow rule and with both nonlinear kinematic and isotropic hardening). Method implementation using a cutting plane algorithm is presented in its general framework and then illustrated by the example of a J2‐plasticity material model considering linear kinematic and isotropic hardening. The approach is compared with the same J2‐plasticity model that has been directly derived from a projection of its equations onto the plane stress subspace. The performance of the multi‐surface plasticity method is shown through the comparison of iso‐error and iso‐step contours in both formulations, and lastly with a case study considering a hollow plate subjected to tension. Copyright © 2014 John Wiley & Sons, Ltd.