Kjell Magne Mathisen

DYNAMIC RESPONSE AND FLUID/STRUCTURE INTERACTION OF SUBMERGED FLOATING TUNNELS

Abstract Alternative approaches to stochastic dynamic response analysis of submerged floating tunnels subjected to wave loading are presented. For the purpose of establishing force, damping and mass coefficients for structural elements with three-dimensional flow conditions, fluid/structure interaction is modeled as finite element implementation of the Navier–Stokes equation. The numerical examples emphasize the effects of wave direction, shortcrestedness, damping, geometrical stiffness and frequency dependence in mass and damping coefficients.

ERROR ESTIMATION AND ADAPTIVITY IN EXPLICIT NONLINEAR FINITE ELEMENT SIMULATION OF QUASI-STATIC PROBLEMS

Abstract A program module for error estimation with application to nonlinear finite element (FE) analysis of shell structures is coupled with the adaptive solution procedure in the explicit FE code LS-DYNA. The error estimation module provides estimates of the local and global errors and element-level refinement indicators. Hence, selective refinement of the mesh in areas where the local error is relatively large compared with a user-defined tolerance is made possible. Furthermore, the relative global error is estimated giving a measure of the overall accuracy of the FE model. Projection-type error estimators based on the L2-norm of the stress vector and the accumulated plastic strain are used to predict the discretization error by comparison of the FE solution with an improved C0-continuous solution obtained by the SPR-method. Three example problems including both material and geometric nonlinearities are provided. The numerical results show that the error estimates capture phenomena such as diffuse necking and local buckling, and give meshes with high resolution in areas with large deformations or high stress gradients.

SUPERCONVERGENT PATCH RECOVERY FOR PLATE PROBLEMS USING STATICALLY ADMISSIBLE STRESS RESULTANT FIELDS

In this paper, we study an approach for recovery of an improved stress resultant field for plate bending problems, which then is used for a posteriori error estimation of the finite element solution. The new recovery procedure can be classified as Superconvergent Patch Recovery (SPR) enhanced with approximate satisfaction of interior equilibrium and natural boundary conditions. The interior equilibrium is satisfied a priori over each nodal patch by selecting polynomial basis functions that fulfil the point-wise equilibrium equations. The natural boundary conditions are accounted for in a discrete least-squares manner. The performance of the developed recovery procedure is illustrated by analysing two plate bending problems with known analytical solutions. Compared to the original SPR-method, which usually underestimates the true error, the present approach gives a more conservative error estimate. Copyright

MULTILEVEL AGGREGATION METHOD FOR SOLVING LARGE-SCALE GENERALIZED EIGENVALUE PROBLEMS IN STRUCTURAL DYNAMICS

In this paper a novel iterative method of multilevel type for solving large-scale generalized eigenvalue problems encountered in structural dynamics is presented. A preconditioned iterative technique, which can be viewed as a modification of the Subspace Iteration method, is used for simultaneous calculation of a group of lowest modes and frequencies. The paper demonstrates that a coarse aggregation model can be employed in the hierarchical structure of the preconditioner in order to provide a good resemblance of the latter to the stiffness matrix of the finite element approximation with respect to low-frequency modes. This leads to a fast convergent procedure of subspace iterations. As opposed to the coarse grid used in methods of multigrid type, this model allows for solving problems with different finite elements including reticulated structures in the framework of large comprehensive finite element software systems. Numerical experiments performed for three-dimensional truss, frame and solid structures demonstrate an excellent performance of the method.

Interactive-adaptive geometrically nonlinear analysis of shell structures

This paper presents an investigation of interactive-adaptive techniques for nonlinear finite element structural analysis. In particular, effective methods leading to reliable automated, finite element solutions of nonlinear shell problems are of primary interest here. This includes automated adaptive nonlinear solution procedures based on error estimation and adaptive step length control, reliable finite elements that account for finite deformations and finite rotations, three-dimensional finite element modeling, and an easy-to-use, easy-to-learn graphical user interface with three-dimensional graphics. A computational environment, which interactively couples a comprehensive geometric modeler, an automatic three-dimensional mesh generator and an advanced nonlinear finite element analysis program with real-time computer graphics and animation tools, is presented. Three examples illustrate the merit and potential of the approaches adopted here and confirm the feasibility of developing fully automated computer aided engineering environments.

Computational Engineering Analysis and Design with ALE-VMS and ST Methods

Flows with moving interfaces include fluid–structure interaction (FSI) and quite a few other classes of problems, have an important place in engineering analysis and design, and pose significant computational challenges. Bringing solution and analysis to them motivated the Deforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) method and also the variational multiscale version of the Arbitrary Lagrangian–Eulerian method (ALE-VMS). These two methods and their improved versions have been applied to a diverse set of challenging problems with a common core computational technology need. The classes of problems solved include free-surface and two-fluid flows, fluid–object and fluid–particle interaction, FSI, and flows with solid surfaces in fast, linear or rotational relative motion. Some of the most challenging FSI problems, including parachute FSI, wind-turbine FSI and arterial FSI, are being solved and analyzed with the DSD/SST and ALE-VMS methods as core technologies. Better accuracy and improved turbulence modeling were brought with the recently-introduced VMS version of the DSD/SST method, which is called DSD/SST-VMST (also ST-VMS). In specific classes of problems, such as parachute FSI, arterial FSI, ship hydrodynamics, fluid–object interaction, aerodynamics of flapping wings, and wind-turbine aerodynamics and FSI, the scope and accuracy of the modeling were increased with the special ALE-VMS and ST techniques targeting each of those classes of problems. This article provides an overview of how the core and special ALE-VMS and ST techniques are used in computational engineering analysis and design. The article includes an overview of three of the special ALE-VMS and ST techniques, which are just a few examples of the many special techniques that complement the core methods. The impact of the ALE-VMS and ST methods in engineering analysis and design are shown with examples of challenging problems solved and analyzed in parachute FSI, arterial FSI, ship hydrodynamics, aerodynamics of flapping wings, wind-turbine aerodynamics, and bridge-deck aerodynamics and vortex-induced vibrations.