Efficient design sensitivity derivatives for multi-load case structures as an integrated part of finite element analysis

In most structural optimization problems the accurate calculation of design sensitivity derivatives is required many times during the optimization process. For large structures with multi-load cases the computational costs are sometimes prohibitive. In this paper an approach for incorporating design sensitivity calculations into the finite element analysis of multi-load case structures is presented. A formulation designed to minimize the computational time for the assembled stiffness matrix derivatives is discussed for different element types. The formulation depends on the implicit differentiation method and requires few additional calculations to obtain the design sensitivity derivatives. The approach is developed and implemented to calculate the design sensitivities for continuum and structural isoparametric elements. To demonstrate the accuracy and efficiency of the developed approach some test cases using different structural and continuum element types are presented.     

Second-order shape design sensitivity using P-version finite element analysis

Thep-version finite element analysis (FEA) approach is attractive for design sensitivity analysis (DSA) and optimization due to its high accuracy of analysis results, even with coarse mesh; insensitivity to finite element mesh distortion and aspect ratio; and tolerance for large shape design changes during design iterations. A continuum second-order shape DSA formulation is derived and implemented usingp-version FEA. The second-order shape design sensitivity can be used for reliability based analysis and design optimization by incorporating it with the second-order reliability analysis method (SORM). Both the second-order shape DSA formulations with respect to the single and mixed shape design parameters are derived for elastic solids using the material derivative concept. Both the direct differentiation and hybrid methods are presented in this paper. A shape DSA is implemented by using an establishedp-version FEA code, STRESS CHECK. Two numerical examples, a connecting rod and bracket, are presented to demonstrate the feasibility and accuracy of the proposed seond-order shape DSA approach.     

Recent advances in non-probabilistic approaches for non-deterministic dynamic finite element analysis

Summary There is a growing awareness of the impact of non-deterministic model properties on the numerical simulation of physical phenomena. These non-deterministic aspects are of great importance when there is a large amount of information to be retrieved from the numerical analysis, as for instance in a numerical reliability study or reliability based optimisation during a design process. Therefore, the non-deterministic properties form a primordial part of a trustworthy virtual prototyping environment. The implementation of such a virtual prototyping environment requires the inclusion of non-deterministic properties in the numerical finite element framework. This articel gives an overview of the emerging non-probabilistic approaches for non-deterministic numerical analysis, and compares them to the classical probabilistic methodology. Their applicability in the context in engineering design is discussed. The typical implementation strategies applied in literature are reviewed. A new concept is introduced for the calculation of envelope frequency response functions. This method is explained in detail and illustrated on a numerical example.     

Studies on two concurrent solvers for finite element analysis

This paper describes a study carried out on the development and implementation of two parallel equation solvers for static finite element analysis. The two direct solvers, one for banded storage and the other for skyline profile storage, are implemented on a tightly coupled shared memory system. Certain key issues like (algorithmic) portability across different parallel architectures, matrix sparsity and vectorisation have been kept in mind while designing the algorithms. Performance studies have been conducted by varying the number of processors and the size of the problem. The results indicate that higher efficiencies can be obtained with both the algorithms described in this paper. However, one has to obtained with both the algorithms described in this paper. However, one has to choose the appropriate solver based on the concurrent approach chosen for paralleling the finite element code. The pseudo-codes, the concurrent implementation of the two solvers, both for shared and message passing systems are presented.     

Efficient approaches to finite element analysis in earthquake engineering

This paper deals with the modeling of reinforced concrete structures subjected to earthquake ground motion. Due to the complex behavior of both materials and structures, efficient numerical tools are developed herein in order to keep accuracy and robustness for large scale computations. We focus our attention on the use of simplified multifiber beam element describing the response of structural components and on macro-element accounting for soil-structure interaction.     

Constraint relation implementation for finite element analysis from an element basis

A procedure for implementing constraint relations among finite element nodal degrees of freedom is outlined. Rather than imposing the constraint relations on the global stiffness or mass matrix as the conventional approach, this procedure is based on the element formulation level in that the element matrices and vectors are properly converted to account for the effect of constraint relations before the global assemblage phase. Adjustment of the global matrix profile for constraint relations and matrix pivoting in equation solving are thus avoided, and the approach can be easily incorporated into existing program systems. In this paper, the theoretical treatment for the proposed procedure is given, and the software implementation aspects are also discussed.     

车身零件预装变形有限元虚拟评估分析

在车身工艺同步工程阶段,通过有限元仿真方法对车身制造过程中预装零件的不同产品设计方案进行虚拟评估分析,根据分析结果指导零件设计优化.该仿真方法在生产实物阶段得到验证,可提前识别制造过程质量风险.与传统的通过经验评估判断零件预装变形的方法相比,在工艺同步工程中应用有限元仿真技术,为解决车身制造过程中的复杂工况变形问题提供理论分析方法和依据,可靠性高,并达到缩短制造周期、降低制造成本的目的 .     

Mesh convergence test system in integrated platform environment for finite element analysis

The Journal of Supercomputing - We designed integrated computer-aided engineering (CAE) middleware with a CAE solution for modeling and simulation work to reduce the cost and time of product...     

Optimum structural design with parallel finite element analysis

Structural analysis is an important part of the optimum structural design process. Therefore, extra effort should be devoted to make this part as efficient as possible. Since finite element analysis is the most powerful and widely used tool in the structural analysis field, in this paper a new method for structural optimization by parallel finite element method is presented. This method divides the original structure into several substructures and assigns each substructure to one processor. Each processor handles its finite element calculation independently with limited communication between processors. Some numerical examples on the Cray X-MP multiprocessor system with their obtained speedups are presented.     

Comparison of two different PNN training approaches for satellitecloud data classification

Presents a training algorithm for probabilistic neural networks (PNN) using the minimum classification error (MCE) criterion. A comparison is made between the MCE training scheme and the widely used maximum likelihood (ML) learning on a cloud classification problem using satellite imagery data.     

Comparison of boundary element and finite element methods for dynamic analysis of elastoplastic plates

Boundary and finite element methodologies for the determination of the response of inelastic plates are compared and critically discussed. Flexural dynamic plate bending problems are considered and a hardening elastoplastic constitutive model is used to describe material behaviour. The domain/boundary element methodology using linear boundary and quadratic interior elements and the finite element method with quadratic Mindlin plate elements are used in this work. The discretized equations of motion in both methodologies are solved by an efficient step-by-step time integration algorithm. Numerical results obtained are presented and compared in order to access the accuracy and computational efficiency of the two methods. In order to make the comparison as meaningful as possible, boundary and finite element computer codes developed by the author are used in this paper. In general, boundary elements appear to be a better choice than finite elements with respect to computational efficiency for the same level of accuracy.     

Variational geometry: A new method for modifying part geometry for finite element analysis

Interactive graphic methods have the potential to significantly reduce the cost associated with pre- and post-processing of finite element analyses. One area of particular importance is the creation and modification of part geometry.

This paper describes a powerful method for modification of geometry for finite element analysis pre-processors. The method, called “Variational Geometry”, uses a single representation to describe the entire family of geometries that share a generic shape.

A solid geometric model of a component is defined with respect to a set of scalar parameters. Dimensions, such as those which appear on a mechanical drawing, are treated as constraints on the permissible values of these parameters. Constraints on the geometry are expressed as a set of non-linear algebraic equations. The values of the parameters and hence the geometry may be determined by solving the set of non-linear constraint equations.

A procedure for minimizing the computational requirements is presented. For a part with n degrees of freedom, the solution time is shown to be O(n).     

An analysis of an implicit finite element algorithm for geometrically nonlinear problems of structural dynamics part 1. Stability

A series of implicit finite element algorithms for the geometrically nonlinear structural dynamics problem are proposed. The proposed algorithms require only the solution of a linear system at each time step. Thus, they are computationally efficient. In addition, the algorithms are discrete conservation laws. The conservative nature of the proposed schemes has a positive effect in providing a stable approximation. The stability of the algorithms is analyzed using energy methods. One of the proposed computational methods is shown to be unconditionally stable.     

An analysis of an implicit finite element algorithm for geometrically nonlinear problems of structural dynamics part 2. Accuracy

In part 1¹ a series of implicit finite element algorithms for the geometrically nonlinear structural problem were proposed. These algorithms were shown to be computationally efficient because they require the solution of a linear system rather than a nonlinear system at each time point. In addition, because of the conservative nature of the algorithms, their stability properties are easily assessed. One algorithm was shown to be unconditionally stable.In part 2 the convergence of the proposed algorithms is demonstrated. It is shown that for the consistent algorithm, additional conditions must be satisfied to insure convergence. In fact, one of the proposed algorithms is shown to be unconditionally stable but conditionally convergent.     

Nonlinear finite element analysis of an autofrettage process

Generally metal forming processes are nonlinear problems. A method is presented to calculate stress and deformation time history and residual states of a mechanically autofrettaged thick walled cylinder. The finite-element-model and the results of the nonlinear analysis are demonstrated.     

Optimum design of plano-milling machine structure using finite element analysis

The problem of optimum design of plano-milling machine structure is formulated as a nonlinear mathematical programming problem with the objective of minimizing the structural weight. The plano-milling machine structure is idealized with triangular plate elements and three dimensional frame elements based on finite element displacement method. Constraints are placed on static deflections and principal stresses in the problem formulation. The optimization problem is solved by using an interior penalty function method in which the Davidon-Fletcher-Powell variable metric unconstrained minimization technique and cubic interpolation method of one dimensional search are employed. A numerical example is presented for demonstrating the effectiveness of the procedure outlined. The results of sensitivity analysis conducted with respect to design variables and fixed parameters about the optimum point are also reported.     

有限元在心脏瓣膜支架设计中的应用

通过SolidWorks建立某心脏瓣膜支架的三维模型,用Abaqus对瓣膜支架压握入鞘过程与疲劳情况进行分析,得到支架的应变分布和疲劳性能.结果可以判断支架设计的优劣,为支架优化设计提供参考.     

Shape sensitivity analysis using a fixed basis function finite element approach

An approach is presented for the determination of solution sensitivity to changes in problem domain or shape. A finite element displacement formulation is adopted and the point of view is taken that the finite element basis functions and grid are fixed during the sensitivity analysis; therefore, the method is referred to as a “fixed basis function” finite element shape sensitivity analysis. This approach avoids the requirement of explicit or approximate differentiation of finite element matrices and vectors and the difficulty or errors resulting from such calculations. Effectively, the sensitivity to boundary shape change is determined exactly; thus, the accuracy of the solution sensitivity is dictated only by the finite element mesh used. The evaluation of sensitivity matrices and force vectors requires only modest calculations beyond those of the reference problem finite element analysis; that is, certain boundary integrals and reaction forces on the reference location of the moving boundary are required. In addition, the formulation provides the unique family of element domain changes which completely eliminates the inclusion of grid sensitivity from the shape sensitivity calculation. The work is illustrated for some one-dimensional beam problems and is outlined for a two-dimensional C⁰ problem; the extension to three-dimensional problems is straight-forward. Received December 5, 1999?Revised mansucript received July 6, 2000     

Support system for finite element analysis

This paper describes work aimed at developing an intelligent support system for finite element modeling and a methodology for managing input data model. Analyzing various statement structures of input data, three structural interface models — the hierarchical browser, the spread sheet and the model generator — are proposed for advanced representation and editing. Two knowledge models composed of macro visual data representation (user oriented model) and micro regularized data representation (processor oriented model) are revealed in conformity with the approach of object-orientation. Moreover, an extended relational schema composed of a composite object (assembly of functional elements) and several abstracted scalar indexes has been implemented for case retrieval.