Academic literature on the topic 'Structural Optimization, Geometric Property and Shape Optimization, Aerospace Structures, Finite Element Method'

This paper is an extension of our recent work that presents a two-scale design method of porosity-like materials using adaptive geometric components. The adaptive geometric components consist of two classes of geometric components: one describes the overall structure at the macrostructure and the other describes the structure of the material at the microstructures. A smooth Heaviside-like elemental-density function is obtained by projecting these two classes on a finite element mesh, namely fixed to reduce meshing computation. The method allows simultaneous optimization of both the overall shape of the macrostructure and the material structure at the micro-level without additional techniques (i.e., material homogenization), connection constraints, and local volume constraints, as often seen in most existing methods. Some benchmark structural design problems are investigated and a selected design is post-processed for 3D printing to validate the effectiveness of the proposed method.
 Keywords:
 topology optimization; concurrent optimization; porosity structures; two-scale topology optimization; adaptive geometric components.

Purpose The purpose of this paper is to present some of the key achievements. At DLR, a sophisticated interdisciplinary aircraft design process is being developed, using the CPACS data format (Nagel et al., 2012; Scherer and Kohlgrüber, 2016) as a means of exchanging results. Within this process, TRAFUMO (Scherer et al., 2013) (transport aircraft fuselage model), built on ANSYS and the Python programming language, is the current tool for automatic generation and subsequent sizing of global finite element fuselage models. Recently, much effort has gone into improving the tool performance and opening up the modeling chain to further finite element solvers. Design/methodology/approach Much functionality has been shifted from specific routines in ANSYS to Python, including the automatic creation of global finite element models based on geometric and structural data from CPACS and the conversion of models between different finite element codes. Furthermore, a new method for modeling and interrogating geometries from CPACS using B-spline surfaces has been introduced. Findings Several new modules have been implemented independently with a well-defined central data format in place for storing and exchanging information, resulting in a highly extensible framework for working with finite element data. The new geometry description proves to be highly efficient while also improving the geometric accuracy. Practical implications The newly implemented modules provide the groundwork for a new all-Python model generation chain, which is more flexible at significantly improved runtimes. With the analysis being part of a larger multidisciplinary design optimization process, this enables exploration of much larger design spaces within a given timeframe. Originality/value In the presented paper, key features of the newly developed model generation chain are introduced. They enable the quick generation of global finite element models from CPACS for arbitrary solvers for the first time.

In recent years, the functionally graded materials (FGM) with cellular structure have become a hot spot in the field of materials research. For the continuously varying cellular structure in the layer-wise FGM, the connection of gradient cellular structures has become the main problem. Unfortunately, the effect of gradient connection method on the overall structural performance lacks attention, and the boundary mismatch has enormous implications. Using the homogenization theory and the level set method, this article presents an efficient topology optimization method to solve the connection issue. Firstly, a simple but efficient hybrid level set scheme is developed to generate a new level set surface that has the partial features of two candidate level sets. Then, when the new level set surface is formed by considering the level set functions of two gradient base cells, a special transitional cell can be constructed by finding the zero level set of this generated level set surface. Since the transitional cell has the geometric features of two gradient base cells, the shape of the transitional cell fits perfectly with its connected gradient cells on both sides. Thus, the design of FGM can have a smooth connectivity with C1 continuity without any complex numerical treatments during the optimization. A number of examples on both 2D and 3D are provided to demonstrate the characteristics of the proposed method. Finite element simulation has also been employed to calculate the mechanical properties of the designs. The simulation results show that the FGM devised by the proposed method exhibits better mechanical performances than conventional FGM with only C0 continuity.

Many structures in the real world show nonlinear responses. The nonlinearity may be due to some reasons, such as nonlinear material (material nonlinearity), large deformation of the structures (geometric nonlinearity), or contact between the parts (contact nonlinearity). Conventional optimization algorithms considering the nonlinearities are fairly difficult and expensive because many nonlinear analyses are required. It is quite difficult to perform topology optimization considering nonlinear static behavior because of the many design variables. In the current element density based topology optimization considering nonlinear behavior, low-density finite elements cause serious numerical problems due to excessive mesh distortion. Updating the material of the finite elements based on the density is considerably complicated because of the relationship between the element density and structural material. The equivalent static loads method for nonlinear static response structural optimization (ESLSO) has been proposed for size and shape optimization. The equivalent static loads (ESLs) are defined as the linear static load sets which generate the same displacement field from nonlinear static analysis. In this research, a new algorithm is proposed for topology optimization considering all kinds of nonlinearities by modifying the existing ESLSO. The new ESLSO can overcome the difficulties which may occur in topology optimization with nonlinear static behavior. A nonlinear static response optimization problem is converted to cyclic use of linear static response optimization with ESLs. Therefore, the new ESLSO can generate results of nonlinear static response topology optimization by using well established nonlinear static analysis and linear static response topology optimization methods. Four structural examples are demonstrated using the finite element method. Different kinds of nonlinearities are involved in each example.

Abstract Lightweight lattice structure generation and topology optimization (TO) are common design methodologies. In order to further improve potential structural stiffness of lattice structures, a method combining the multi-topology lattice structure design based on unit-cell library with topology optimization is proposed to optimize the parts. First, a parametric modeling method to rapidly generate a large number of different types of lattice cells is presented. Then, the unit-cell library and its property space are constructed by calculating the effective mechanical properties via a computational homogenization methodology. Third, the template of compromise Decision Support Problem (cDSP) is applied to generate the optimization formulation. The selective filling function of unit cells and geometric parameter computation algorithm are subsequently given to obtain the optimum lightweight lattice structure with uniformly varying densities across the design space. Lastly, for validation purposes, the effectiveness and robustness of the optimized results are analyzed through finite element analysis (FEA) simulation.

In this thesis, structural optimization study is performed by using three different methods. In the first method, optimization is performed using MSC.NASTRAN Optimization Module, a commercial structural analysis program. In the second method, optimization is performed using the optimization code prepared in MATLAB and MSC.NASTRAN as the solver. As the third method, optimization is performed by using the optimization code prepared in MATLAB and analytical equations as the solver. All three methods provide certain advantages in the solution of optimization problems. Therefore, within the context of the thesis these methods are demonstrated and the interface codes specific to the programs used in this thesis are explained in detail. In order to compare the results obtained by the methods, the verification study has been performed on a cantilever beam with rectangular cross-section. In the verification study, the height and width of the cross-section of the beam are taken as the two design parameters. This way it has been possible to show the design space on the two dimensional graph, and it becomes easier to trace the progress of the optimization methods during each step. In the last section structural optimization of a multi-element wing torque box has been performed by the MSC.NASTRAN optimization module. In this section geometric property optimization has been performed for constant tip loading and variable loading along the wing span. In addition, within the context of shape optimization optimum rib placement problem has also been solved.

Finite Element Analysis or Finite Element Method is based on the principle of dividing a structure into a finite number of small elements. It is a sophisticated engineering tool, which has been used extensively in design optimization and structural analysis first originated in the aerospace industry to study stress in complex airframe structures. This method is a way of getting a numerical solution to a specific problem, used to analyze stresses and strains in complex mechanical systems. It enables the mathematical conversion and analysis of mechanical properties of a geometric object with wide range of applications in dental and oral health science. It is useful for specifying predominantly the mechanical aspects of biomaterials and human tissues that cannot be measured in vivo. It has various advantages, can be compared with studies on real models, and the tests are repeatable, with accuracy and without ethical concerns.

We look to expand the reach of continuum topology optimization to include the design of ‘structures’ that gain functionality or are specifically manufactured from discrete, non-overlapping objects. While significant advancements have been made in restricting the geometric properties of topology-optimized structures, including restricting the minimum and maximum length scale of features, continuum topology optimization is still largely limited to monolithic structures. A wide variety of structures and materials, however, gain their stiffness or functionality from discrete objects, such as fiber-reinforced composites. This work examines a recently developed method for optimizing the distribution of discrete objects (2d inclusions) across a design domain and extends the approach to variable shape and variable sized objects that must be selected from a designer-defined set. This essentially enables simultaneous optimization of object sizes, shapes, and/or locations within the projection framework, without need for additional constraints. As in traditional topology optimization, gradient-based optimizers are used with sensitivity information estimated via the adjoint method, solved using finite element analysis. The algorithm is demonstrated on benchmark problems in structural design for the case where the objects are stiff inclusions embedded in a compliant matrix material.

Fifty years ago, the railcar industry relied entirely on classical analysis methods using fundamental solid mechanics theory to establish design and manufacturing protocols. While this method produced working designs, the assumptions required by this type of analysis often led to overdesigned railcars. In the 1950s, the generalized mathematical approach of Finite Element Analysis (FEA) was developed to model the structural behaviors of mechanical systems. FEA involves creating a numerical model by discretizing a continuous system into a finite system of grid divisions. Each grid division, or element, has an inherent geometric shape and each element is comprised of points which are referred to as nodes. The connected pattern of nodes and elements is called a mesh. A solver organizes the mesh into a matrix of differential equations and computes the displacements using linear algebraic operations from which strains and stresses are obtained. The rapid development of computing technology provided the catalyst to drive FEA from research into industry. FEA is currently the standard approach for improving product design cycle times that were previously achieved by trial and error. Moreover, simulation has improved design efficiency allowing for greater advances in weight, strength, and material optimization. While FEA had its roots planted in the aerospace industry, competitive market conditions have driven simulation into many other professional fields of engineering. For the last few decades, FEA has become essential to the submittal of new railcar designs for unrestricted interchange service across North America. All new railcar designs must be compliant to a list of structural requirements mandated by the Association of American Railroads (AAR), which are listed in its MSRP (Manual of Standards and Recommended Practices) in addition to recommended practices in Finite Element (FE) modeling procedures. The MSRP recognizes that these guidelines are not always feasible to completely simulate, allowing the analyst to justify situations where deviations are necessary. Benefits notwithstanding, FEA has inherent challenges. It is understood that FEA does not provide exact solutions, only approximations. While FEA can provide meaningful insight into actual physical behavior leading to shorter development times and lower costs, it can also create bogus solutions that lead to potential safety and engineering risks. Regardless of how appropriate the FEA assumptions may be, engineering judgment is required to interpret the accuracy and significance of the results. A constant balance is made between model fidelity and computational solve time. The purpose of this paper is to discuss the FEA approach to railcar analysis that is used by BNSF Logistics, LLC (BNSFL) in creating AAR compliant railcar designs. Additionally, this paper will discuss the challenges inherent to FEA using experiences from actual case studies in the railcar industry. These challenges originate from assumptions that are made for the analysis including element types, part connections, and constraint locations for the model. All FEA terminology discussed in this paper is written from the perspective of an ANSYS Mechanical user. Closing remarks will be given about where current advances in FEA technology may be able to further improve railcar industry standards.