Design of actively-cooled microvascular materials: a genetic algorithm inspired network optimization

Structural and Multidisciplinary Optimization - The design of a microvascular flow network embedded in an actively-cooled polymeric material is presented. A multi-objective Genetic Algorithm (GA)...     

On using exponential basis functions for laminates modeled by CLPT,FSDT and TSDT: Further tests and results

In this paper we present some results from the application of a mesh-free method introduced previously (Compos Struct 2011;93:3112–9 and 94:84–91) for bending analysis of laminated composite plates. This method is applicable to a wide range of bending problems without limitation in the stacking sequence of the laminated plates and the boundary conditions. Herein, two specific types of problems, having traction free boundaries, are examined and the issues related to the solution of them are addressed. Also as new benchmark problems, some more results for cross-ply and angle-ply composites are presented.     

Computational modeling and design of actively-cooled microvascular materials

The computational modeling and design of an actively-cooled microvascular fin specimen is presented. The design study is based on three objective functions: (i) minimizing the maximum temperature in the thermally loaded fin, (ii) optimizing the flow efficiency of the embedded microchannel, and (iii) minimizing the void volume fraction of the microvascular material. A recently introduced Interface-enriched Generalized Finite Element Method (IGFEM) is employed to evaluate the temperature field in a 2D model of the specimen, allowing for the accurate and efficient capturing of the gradient discontinuity along the fluid/solid interface without the need of meshes that conform to the geometry of the problem. Finding the optimal shape of the embedded microchannel is thus accomplished with a single non-conforming mesh for all configurations. Prior to the optimization study, the IGFEM solver is validated through comparison with infrared measurements of the thermal response of an epoxy fin with a sinusoidal microchannel.     

On the application of higher‐order elements in the hierarchical interface‐enriched finite element method

This article introduces a new algorithm for evaluating enrichment functions in the higher‐order hierarchical interface‐enriched finite element method (HIFEM), which enables the fully mesh‐independent simulation of multiphase problems with intricate morphologies. The proposed hierarchical enrichment technique can accurately capture gradient discontinuities along materials interfaces that are in close proximity, in contact, and even intersecting with one another using nonconforming finite element meshes for discretizing the problem. We study different approaches for creating higher‐order HIFEM enrichments corresponding to six‐node triangular elements and analyze the advantages and shortcomings of each approach. The preferred method, which yields the lowest computational cost and highest accuracy, relies on a special mapping between the local and global coordinate systems for evaluating enrichment functions. A comprehensive convergence study is presented to show that this method yields similar convergence rate and precision as those of the standard FEM with conforming meshes. Finally, we demonstrate the application of the higher‐order HIFEM for simulating the thermal and deformation responses of several materials systems and engineering problems with complex geometries. Copyright © 2015 John Wiley & Sons, Ltd.     

A mesh-free method using exponential basis functions for laminates modeled by CLPT,FSDT and TSDT – Part I: Formulation

In this part of the paper, we introduce a meshfree approach for static analysis of isotropic/orthotropic cross-ply laminated plates with symmetric/non-symmetric layers. In this method, the solution is first split into homogenous and particular parts and then the homogenous part is approximated by the summation of an appropriately selected set of exponential basis functions (EBFs) that are restricted to satisfy the governing partial differential equation (PDE). The particular solution is derived using a similar approach and another series of EBFs. The imposition of the boundary conditions is performed by a collocation method through a discrete transformation technique. The solution method allows us to obtain semi-analytical solution of plate problems with various shapes and boundary conditions. Although implemented for cross-ply laminates in this work, the proposed method is applicable to more general lamination cases as long as the governing PDEs are of constant coefficient type. This part of the paper is devoted to the basic features of the formulation and the evaluation of the EBFs using classical, first and third order shear deformation theories. Explicit expressions are given for special cases for further use.     

An interface‐enriched generalized FEM for problems with discontinuous gradient fields

A new generalized FEM is introduced for solving problems with discontinuous gradient fields. The method relies on enrichment functions associated with generalized degrees of freedom at the nodes generated from the intersection of the phase interface with element edges. The proposed approach has several advantages over conventional generalized FEM formulations, such as a lower computational cost, easier implementation, and straightforward handling of Dirichlet boundary conditions. A detailed convergence study of the proposed method and a comparison with the standard FEM are presented for heat transfer problems. The method achieves the optimal rate of convergence using meshes that do not conform to the interfaces present in the domain while achieving a level of accuracy comparable to that of the standard FEM with conforming meshes. Various application problems are presented, including the conjugate heat transfer problem encountered in microvascular materials. Copyright © 2011 John Wiley & Sons, Ltd.     

A mesh-free method using exponential basis functions for laminates modeled by CLPT, FSDT and TSDT – Part II: Implementation and results

In this part of the paper we give the details of the implementation of the method presented in the first part. Also the solutions of several benchmark plate problems with various geometries are presented to validate the results. It has been observed that the method can perform excellently in a wide range of problems defined for the bending analysis of laminated plates based on various plate theories. For further use, some explicit expressions are given for the exponential basis functions suitable for the solution of symmetric cross-ply laminates.     

A Trefftz method in space and time using exponential basis functions: Application to direct and inverse heat conduction problems

In this paper we present a Trefftz method based on using exponential basis functions (EBFs) to solve one (1D) and two (2D) dimensional transient problems. We focus on direct and inverse heat conduction problems, the latter being the more challenging ones, to show the capabilities of the method. A summation of exponential basis functions (EBFs), satisfying the governing equation in time and space, with unknown coefficients is considered for the solution. The unknown coefficients are determined by the satisfaction of the prescribed time dependent boundary and initial conditions through a collocation method. Several 1D and 2D direct and inverse heat conduction problems are solved. Some numerical evidence is provided for the convergence and sensitivity of the method with respect to the noise levels of the measured data and time steps.     

Exponential basis functions in solution of static and time harmonic elastic problems in a meshless style

In this paper, exponential basis functions (EBFs) are used in a boundary collocation style to solve engineering problems whose governing partial differential equations (PDEs) are of constant coefficient type. Complex‐valued exponents are considered for the EBFs. Two‐dimensional elasto‐static and time harmonic elasto‐dynamic problems are chosen in this paper. The solution procedure begins with first finding a set of appropriate EBFs and then considering the solution as a summation of such EBFs with unknown coefficients. The unknown coefficients are determined by the satisfaction of the boundary conditions through a collocation method with the aid of a consistent and complex discrete transformation technique. The basis and various forms of the transformation have been addressed and discussed. We shall propose several strategies for selection of EBFs with the aid of the basis explained for the transformation. While using the transformation, the number of EBFs should not necessarily be equal to (or less than) the number of boundary information data. A library of EBFs has also been presented for further use. The effect of body forces is included in the solution via construction of particular solution by the use of the discrete transformation and another series of EBFs. A number of sample problems are solved to demonstrate the capabilities of the method. It has been shown that the time harmonic problems with high wave number can be solved without much effort. The method, categorized in meshless methods, can be applied to many other problems in engineering mechanics and general physics since EBFs can easily be found for almost all problems with constant coefficient PDEs. Copyright © 2009 John Wiley & Sons, Ltd.