Anton Tkachuk

Level Set Topology Optimization of Printed Active Composites

Multimaterial polymer printers allow the placement of different material phases within a composite, where some or all of the materials may exhibit an active response. Utilizing the shape memory (SM) behavior of at least one of the material phases, active composites can be three-dimensional (3D) printed such that they deform from an initially flat plate into a curved structure. This paper introduces a topology optimization approach for finding the spatial arrangement of shape memory polymers (SMPs) within a passive matrix such that the composite assumes a target shape. The optimization approach combines a level set method (LSM) for describing the material layout and a generalized formulation of the extended finite-element method (XFEM) for predicting the response of the printed active composite (PAC). This combination of methods yields optimization results that can be directly printed without the need for additional postprocessing steps. Two multiphysics PAC models are introduced to describe the response of the composite. The models differ in the level of accuracy in approximating the residual strains generated by a thermomechanical programing process. Comparing XFEM predictions of the two PAC models against experimental results suggests that the models are sufficiently accurate for design purposes. The proposed optimization method is studied with examples where the target shapes correspond to a plate-bending type deformation and to a localized deformation. The optimized designs are 3D printed and the XFEM predictions are compared against experimental measurements. The design studies demonstrate the ability of the proposed optimization method to yield a crisp and highly resolved description of the optimized material layout that can be realized by 3D printing. As the complexity of the target shape increases, the optimal spatial arrangement of the material phases becomes less intuitive, highlighting the advantages of the proposed optimization method.

Numerical approaches to stability analysis of cylindrical composite shells based on load imperfections

Purpose – Current procedures of buckling load estimation for thin-walled structures may provide very conservative estimates. Their refinement offers the potential to use structure and material properties more efficiently. Due to the large variety of design variables, for example laminate layup in composite structures, a prohibitively large number of tests would be required for experimental assessment, and thus reliable numerical techniques are of particular interest. The purpose of this paper is to analyze different methods of numerical buckling load estimation, formulate simulation procedures suitable for commercial software and give recommendations regarding their application. All investigations have been carried out for cylindrical composite shells; however similar approaches are feasible for other structures as well. Design/methodology/approach – The authors develop a concept to apply artificial load imperfections with the aim to estimate as good as possible lower bounds for the buckling loads of shel...

APPLICATIONS OF VARIATIONALLY CONSISTENT SELECTIVE MASS SCALING IN EXPLICIT DYNAMICS

Abstract. The aim of Selective Mass Scaling (SMS) in context of non-linear structural mechanics is to increase the critical time-step for explicit time integration without substantial loss in accuracy in the lower modes. The Conventional Mass Scaling (CMS) adds artificial mass only to diagonal terms of the lumped mass matrix and thus preserves diagonal format of mass matrix. It is usually applied in little number of small or stiff elements, like spot-welds in car crash, whose high eigenfrequencies limit time-step. However, translational and rotational inertia of the structure increases, which may cause non-physical phenomena. SMS technique adds artificial terms both to diagonal and non-diagonal terms, which results in non-diagonal mass matrix, but at least allows preservation of translational mass. Thus SMS can be used uniformly in domain with less non-physical artifacts. The previous works on SMS rely on algebraically constructed mass scaling matrices or stiffness proportional mass scaling. These approaches provide very small choice of mass scaling templates and they lack rigorous variational formulation. The goal of this paper is to develop variational basis for SMS with consistent discretization of inertial term and to assess efficiency of the proposed approach.

Reduction of Numerical Sensitivities in Crash Simulations on HPC-Computers (HPC-10)

For practical application in engineering numerical simulations are required to be reliable and reproducible. Unfortunately crash simulations are highly complex and nonlinear and small changes in the initial state can produce big changes in the results. This is caused partially by physical instabilities and partially by numerical instabilities. Aim of the project is to identify the numerical sensitivities in crash simulations and suggest methods to reduce the scatter of the results.

ESTIMATION OF STABILITY LIMIT BASED ON GERSHGORIN'S THEOREM FOR EXPLICIT CONTACT-IMPACT ANALYSIS SIGNORINI PROBLEM USING BIPENALTY APPROACH

Abstract. The stability properties of the bipenalty method presented in Reference [4] is studied in application to one-dimensional bipenalized Signorini problem. The attention has been paid on the critical Courant numbers estimation based on Gershgorin’s theorem. It is shown that Gershgorin’s formula overestimates maximum eigenfrequency for all penalty ratios with exception of the critical penalty ratio. Thus, smaller safer values of critical Courant numbers are obtained in comparison with exact ones calculated from the solution of eigenvalue problem.