In order to deal with the divergence and instability due to the ill-posedness of the nonlinear finite element (FE) model of strain-softening structure in implicit static analysis, the dynamic relaxation method (DRM) was used with kinetic damping to solve the static increments in the incremental solution procedure so that the problem becomes well-posed. Moreover, in DRM there is no need to assemble and inverse the stiffness matrix as in implicit static analysis such that the associated computational cost is avoided. The ascending branch of static equilibrium path was solved by load increments, while the peak point and the descending branch were solved by displacement increments. Two numerical examples illustrated the effectiveness of such application of DRM in the FE analysis of static equilibrium path of strain-softening structures.
The simulation of large deformation contact problems has been a tough subject due to the existence of multiple nonlinearities, including geometric nonlinearity and contact interface nonlinearity. In this paper, we develop a novel method to compute the large deformation of 2D frictionless contact by employing Nitsche-based isogeometric analysis. The enforcement of contact constraints as one of the main issues in contact simulation is implemented by using Nitsche’s method, and the node-to-segment scheme is applied to the contact interface discretization. We detailedly derive the discrete formulations for 2D large deformation frictionless contact where NURBS is used for geometrical modeling and the Neo-Hookean hyperelastic materials are applied to describe the deformation of the model. The collocation method with Greville points is employed to integrate the contact interface and the classical Legendre–Gauss quadrature rule is used for contact bodies’ integration. The Lagrange multiplier method and penalty method are also implemented for comparison with Nitsche’s method. Several examples are investigated, and the obtained results are compared with that from commercial software ABAQUS to verify the effectiveness and accuracy of the Nitsche-based isogeometric analysis.
The prominent properties owned by T-spline, such as flexibility, continuity, local refinement, water tightness, make it extensively applied in CAD & CAE integrating scenarios. But the local fairness may dissatisfy in damaged areas or even on the entire surface of industry applications. Under these circumstances, local protrusion and sharp features appeared seriously affect the fairness of T-spline surfaces. Derived from the geometric properties of T-spline control points, we propose a smoothing algorithm based on the 1-ring neighborhood space angle to deal with local abruptions of T-spline surfaces. We also demonstrate the availability of the proposed algorithm through several experiments. Results show that this method is suitable for removing sharp features and smoothing unstructured T-spline surfaces.
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