Sensitivity analysis with the modified Heaviside function for the optimal layout design of multi-component systems

For electrical impedance tomography (EIT) of brain, the use of anatomically accurate and patient-specific finite element (FE) mesh has been shown to confer significant improvements in the quality of image reconstruction. But, given the lack of a rapid method to achieve the accurate anatomic geometry of the head, the generation of patient-specifc mesh is time-comsuming. In this paper, a m odified fuzzy c-means algorithm based on no n-local means method is performed to implement the segmentation of different layers in the head based on head CT images. This algorithm showed a better effect, especially an accurate recognition of the ventricles and a suitable performance dealing with noise. And the FE mesh established according to the segmentation results is valid ated in computational simulation. So a rapid practicable method can be provided for the generation of patient-specific FE mesh of the human head that is suitable for brain EIT. Keyword: Computerized tomography, image segmentation, mesh generation, electrical impedance tomography

This paper proposes a topology optimization method for a dielectric optical cloak that provides results that are perfectly free from intermediate materials, based on a level set boundary expression and the Finite Element Method. The finite element mesh is re-generated to fit the iso-surface of the level set function at every iterative step, to remove intermediate materials, so that the obtained optimal structure consists of only two materials, the dielectric material and air. First, the level set-based topology optimization is formulated and a topology optimization algorithm is proposed for the exact level set approach. Next, design requirements for the dielectric optimal cloak device are clarified and an objective functional for the design is formulated. The proposed method is then applied to a simple numerical problem to illustrate its effectiveness.

Two approaches to three-dimensional structural topology optimization using level set parameterization with arbitrary finite-element meshes are presented.In both approaches the structural elasticity problem is solved on a fixed finite-element mesh.The shape sensitivities obtained from the solution of the structural problem are mapped to the orthogonal mesh in order to generate the corresponding advection velocities.The first approach superimposes a background Cartesian grid onto the finite element mesh.The level set function is defined on this Cartesian mesh with the advection velocities being taken as a weighted sum of the sensitivities at all nearby structural nodes within a prescribed radius.The second approach defines the level set function on a skewed structured mesh which is coincident with the finite element mesh.The Hamilton-Jacobi equation is then solved in this transformed mesh space and a Jacobian transformation is used create a one-to-one mapping between the structural elements and the nodes of the level set mesh.The two methods are evaluated and compared based upon the results of a benchmark problem involving three-dimensional topology optimization of an aircraft wing structure.The results indicate that the Jabobian mapping method offers a significant advantage over the superposition method, both in terms of convergence time as well as the objective value of the converged solution.

This paper presented a recent work on preform design optimization in bulk metal forming process based on a topological approach. In the paper, to obtain a forging preform shape with reduced material consumption but enhanced uniform material deformation, a new element removal and addition criterion has been established with consideration of hydrostatic stress and strain components. In order to overcome the problem that the size of FE mesh for forging simulation cannot be directly used for topology optimization, background mesh was employed for optimization evolution while coarser but smoother FE mesh was employed for FE simulation. The other key techniques developed include an interpolation method and surface smoothing treatment for jagged surface after element addition and elimination. A C# program for optimization system integrated with DEFORM-3D finite element (FE) software package is developed and an industrial case problem: forging of a 3D aeroengine blade is investigated. Considering the feasibility of producing a preform, different constraints are applied in the optimization process to affect the preform shape. The optimization results are presented and discussed, which suggest that the developed topology optimization method is an efficient approach for 3D preform design and optimization.

A mesh conversion program has been developed to convert EXODUS II-formatted finite element meshes to the ascii format used by the PROTEUS-SN neutronics code developed at Argonne National Laboratory.This manual contains instructions, usage examples, and methodology for the mesh converter.The PROTEUS-SN neutronics code requires a finite element mesh input file in one of several accepted formats (ascii, nemesh, pntmesh, or bgpmesh).None of these file formats are directly produced by conventional finite element file modeling codes, therefore format conversion is required.Currently, most finite element meshes are prepared using the Cubit program developed by Sandia National Laboratory.Cubit can export finite element meshes in a variety of formats including the portable EXODUS II format.EXODUS II files are binary files with NetCDF data storage structures designed to handle large object-oriented arrays.While a specialized EXODUS II application programming interface (API) exists to query EXODUS II data, the general NetCDF API can also be used for the same purpose.The described program improves upon a previous tool which had limited flexibility and performance.Notably, the new converter successfully converts EXODUS II files generated with more recent versions of Cubit (version 13+) and has no limitation on mesh size (total number of vertices or elements).The converter queries data from the EXODUS II file using NetCDF API commands, reads the data in the file, reorganizes it, and writes it to the ascii file format used by PROTEUS-SN.

SummaryIn this work, a reduced‐order model based on adaptive finite element meshes and a correction term obtained by using an artificial neural network (FAN‐ROM) is presented. The idea is to run a high‐fidelity simulation by using an adaptively refined finite element mesh and compare the results obtained with those of a coarse mesh finite element model. From this comparison, a correction forcing term can be computed for each training configuration. A model for the correction term is built by using an artificial neural network, and the final reduced‐order model is obtained by putting together the coarse mesh finite element model, plus the artificial neural network model for the correction forcing term.The methodology is applied to nonlinear solid mechanics problems, transient quasi‐incompressible flows, and a fluid‐structure interaction problem. The results of the numerical examples show that the FAN‐ROM is capable of improving the simulation results obtained in coarse finite element meshes at a reduced computational cost.

The paper deals with the application of an adaptive, hierarchic‐iterative finite element technique to solve two‐dimensional electromechanical boundary value problems with impermeable cracks in piezoelectric plates. In order to compute the dielectric and mechanical intensity factors, the interaction integral technique is used. The iterative finite element solver takes advantage of a sequence of solutions on hierarchic discretizations. Based on an a posteriori error estimation, the finite element mesh is locally refined or coarsened in each step. Two crack configurations are investigated in an infinite piezoelectric plate: A finite straight crack and a finite kinked crack. Fast convergence of the numerical intensity factors to the corresponding analytical solution is exemplarily proved during successive adaptive steps for the first configuration. Similar tendency can be observed for the second configuration. Furthermore, the computed intensity factors for the kinks are found to coincide well with the corresponding analytical values. In order to simulate the kinks spreading from a straight crack, the finite element mesh is modified automatically with a specially developed algorithm. This forms the basis for a fully adaptive simulation of crack propagation. Copyright © 2009 John Wiley & Sons, Ltd.

Three-dimensional cellular automaton-finite element modeling of solidification grain structures for arc-welding processes

The process of shear band formation in plane strain compression of fcc metals: Effects of crystallographic texture

In the bending forming process, it is well known that the relation of the forces and the strains. But it is inexplicit about the dynamic process. This paper analysed the bending forming dynamic process of the pure T2 copper. A finite element mesh is printed on the top end surface of the specimen by a hairline greasy pen. The dynamic process was carried out on a bending machine, and shot by a digital camera. The photos of forming process were processed in order to make the analysis explicitly. Through contrasted the processed photos of the different times, the shape changing could be observed clearly. And the pure T2 copper would be bended more easier in the later period process.

Finite element-based virtual fields method with pseudo-real deformation fields for identifying constitutive parameters

A plasticity model with yield limit degradation is implemented in a boundary element program to study the fracture behavior of quasi-brittle materials. A special integration method is applied to deal with the singular integrations encountered in the volume integrals over internal cells. Strain-softening damage localizations are investigated. It is found that the damage tends to localize into a zone of one cell wide which leads to an incorrect result when different cell meshes are used in the analysis. Some sort of localization limiter has to be incorporated into the analysis in order to achieve meaningful results. INTRODUCTION In the simulation of fracture behavior of quasi-brittle materials such as concrete or ceramics, it is essential to take into account the evolution of a relative large fracture process zone forms in front of the crack tip. The process zone consists of hundreds of microcracks and its overall behavior can generally be simulated either by discrete-cracking models such as the fictitious crack model [4, 5] or smeared-cracking models such as strain-softening damage models [2, 3]. In this paper the fracture process zone is simulated by a plasticity model with yield limit degradation. When the stresses near the crack tip reach the yield surface, the yield surface will contract rather than expand. This results in a decrease in stresses during an increase in strains, i.e., a strain softening. The decrease in stresses simulates a material damage caused by mainly the formation of microcracks. Difficulty has been encountered in the finite element analysis involving strain-softening behavior. As different meshes are used in an analysis, Transactions on Modelling and Simulation vol 2, © 1993 WIT Press, www.witpress.com, ISSN 1743-355X 304 Boundary Elements different results are obtained. The results are not objective with respect to finite element meshes. Also, the energy dissipation of a structure at failure decreases with the refinement of the finite element mesh. It implies that the structure will fail at near zero energy dissipation when a very fine mesh is used. This is in contradiction with the reality. All these problems are considered due to damage localization [1,2,3]. In this paper, the plasticity model with yield limit degradation is incorporated into a boundary element program to study the damage localization problems. Many publications on the boundary element analysis of elastoplastic problems [7-14] have been seen since the first paper on the problem published in 1971 by Swedlow and Cruse [6]. However, the literature on the study of damage localization problems using boundary element approach is rarely seen. The initial stress boundary element method is applied to deal with the nonlinear damage problems, For localization problems, damage tends to localize into a small region of the body, and thus the internal cells required for integration purposes are needed only in a small region rather than the entire body. A special semi-analytical integration method for triangular cell is used to carry out the volume integration over the cell that contains a singular node. A rectangular panel with three different cell meshes are analyzed. It is shown that the results are not objective to the cell meshes even though all other conditions are kept the same. BOUNDARY ELEMENT FORMULATION FOR ELASTOPLASTIC ANALYSIS For elastoplastic problems based on small strain theory, the basic equations in incremental form are as follows: The governing equations are da^ + db* = 0 (1) with boundary conditions du;(x) = (x) x e I (2) cR (x) x e I I + T^T and total strain increment de^ = de^ 4de^= (du + dUjJ/2 (3) where de^ and de^ are elastic and plastic strain increments. T is the boundary of body 0 under consideration, da^ ,db; ,du;, dr; are the stress, body force (per unit volume), displacement, and traction increment respectively. du ± and df j are prescribed displacements and tractions on boundary I and r%. Transactions on Modelling and Simulation vol 2, © 1993 WIT Press, www.witpress.com, ISSN 1743-355X Boundary Elements 305 The yield criterion is F(a%,k)= f(a$ <Kk) = 0 (4) where F and f are yield functions, $ is a work hardening function, and k is the work hardening parameter. The constitutive equations are de'u) = d<^ do, = DV^U (5) where D^= &pvl(l-2v)] 6fo + M<Wji + W

High precision magnetic field computer programs are required to accurately calculate the multipole content and magnetic field strength associated with a given accelerator magnet design. In this work, a specialized version of the finite element computer program WEMAP (Westinghouse Electric and Magnetic Analysis Program) is applied to field harmonic calculations. The computer program relies on a higher-order finite element formulation and high-precision computer representation to minimize calculation error. Several calculations are made for a SSC CDM cross section design. The effects of mesh fineness and finite element order are investigated by examining finite element grids with increasing mesh density and element order. A key feature of this computer program is the capability to minimize the truncation error associated with a finite element mesh by increasing the order of the finite element interpolating polynomial. Finite elements of order one through six are incorporated. Inaccuracies which may occur using the lower-order finite elements with a coarse mesh are identified in this paper. Care must be taken in meshing the yoke iron region to accurately account for field harmonics due to nonuniform iron permeability. Methods of extracting the spatial harmonics from the finite element solution are discussed. The field strength and harmonics are calculated for a full-section model of a CDM magnet cross section.

ABSTRACTIn this article, a novel approach is presented to perform topology optimization in a simple and explicit way. The method capitalizes on the use of a bio-inspired algorithm to represent topology, leading to more flexible optimization solutions along with explicit structure representation. To avoid remeshing upon design changes, a special treatment called the enhanced stiffness transformation approach (ESTA) is introduced to transform the stiffness and mass matrices of the growing stiffener into a set of equivalent stiffness and mass matrices. In this way, stiffeners are separated from the finite element mesh and can grow in an arbitrary direction to form an optimized layout solution. Notably, this approach incorporates more geometric information into topology optimization, which improves the clarity of stiffener layouts. Finally, the effectiveness of the proposed method is illustrated with two examples of maximum eigenfrequency design of plate/shell structures.

An efficient contact algorithm for the interaction of material particles with finite elements