Stiffness analysis of polymeric composites using the finite element method

The ability to predict the mechanical behavior of polymer composites is crucial for their design and manufacture. Extensive studies based on both macro- and micromechanical analyses are used to develop new insights into the behavior of composites. In this respect, finite element modeling has proved to be a particularly powerful tool. In this article, we present a Galerkin scheme in conjunction with the penalty method for elasticity analyses of different types of polymer composites. In this scheme, the application of Green's theorem to the model equation results in the appearance of interfacial flux terms along the boundary between the filler and polymer matrix. It is shown that for some types of composites these terms significantly affect the stress transfer between polymer and fillers. Thus, inclusion of these terms in the working equations of the scheme preserves the accuracy of the model predictions. The model is used to predict the most important bulk property of different types of composites. Composites filled with rigid or soft particles, and composites reinforced with short or continuous fibers are investigated. For each case, the results are compared with the available experimental results and data obtained from other models reported in the literature. Effects of assumptions made in the development of the model and the selection of the prescribed boundary conditions are discussed.

Kinetostatic-model-based Stiffness Analysis of Exechon PKM

As a comparative newly-invented PKM with over-constraints in kinematic chains, the Exechon has attracted extensive attention from the research society. Different from the well-recognized kinematics analysis, the research on the stiffness characteristics of the Exechon still remains as a challenge due to the structural complexity. In order to achieve a thorough understanding of the stiffness characteristics of the Exechon PKM, this paper proposed an analytical kinetostatic model by using the substructure synthesis technique. The whole PKM system is decomposed into a moving platform subsystem, three limb subsystems and a fixed base subsystem, which are connected to each other sequentially through corresponding joints. Each limb body is modeled as a spatial beam with a uniform cross-section constrained by two sets of lumped springs. The equilibrium equation of each individual limb assemblage is derived through finite element formulation and combined with that of the moving platform derived with Newtonian method to construct the governing kinetostatic equations of the system after introducing the deformation compatibility conditions between the moving platform and the limbs. By extracting the 6 x 6 block matrix from the inversion of the governing compliance matrix, the stiffness of the moving platform is formulated. The computation for the stiffness of the Exechon PKM at a typical configuration as well as throughout the workspace is carried out in a quick manner with a piece-by-piece partition algorithm. The numerical simulations reveal a strong position-dependency of the PKM's stiffness in that it is symmetric relative to a work plane due to structural features. At the last stage, the effects of some design variables such as structural, dimensional and stiffness parameters on system rigidity are investigated with the purpose of providing useful information for the structural optimization and performance enhancement of the Exechon PKM. It is worthy mentioning that the proposed methodology of stiffness modeling in this paper can also be applied to other overconstrained PKMs and can evaluate the global rigidity over workplace efficiently with minor revisions.

Stiffness Analysis and Experiment of a Novel 5-DoF Parallel Kinematic Machine Considering Gravitational Effects

In order to carry out high-precision machining of aerospace structural components with large size, thin wall and complex surface, this paper proposes a novel parallel kinematic machine (PKM) and formulates its semi-analytical theoretical stiffness model considering gravitational effects that is verified by stiffness experiments. From the viewpoint of topology structure, the novel PKM consists of two substructures in terms of the redundant and overconstrained parallel mechanisms that are connected by two interlinked revolute joints. The theoretical stiffness model of the novel PKM is established based upon the virtual work principle and deformation superposition principle after mapping the stiffness models of substructures from joint space to operated space by Jacobian matrices and considering the deformation contributions of interlinked revolute joints to two substructures. Meanwhile, the component gravities are treated as external payloads exerting on the end reference point of the novel PKM resorting to static equivalence principle. This approach is proved by comparing the theoretical stiffness values with experimental stiffness values in the same configurations, which also indicates equivalent gravity can be employed to describe the actual distributed gravities in an acceptable accuracy manner. Finally, on the basis of the verified theoretical stiffness model, the stiffness distributions of the novel PKM are illustrated and the contributions of component gravities to the stiffness of the novel PKM are discussed.

Dynamic stiffness analysis of bridge abutments

Strong motion records obtained in instrumented short-span bridges show the importance of the abutments in the dynamic response of the structure. Existing models study the pier foundation influence but not the abutment performance. This work proposes two and three dimensional boundary element models in the frequency domain and studies the dimensionless dynamic stiffness of standard bridge abutments.

Suitability of a point-contact SAW-based stiffness transducer for biomedical applications

Methods of diagnosis in Biomedical applications can be broadly divided into contact and non-contact based methods. So far, ultrasound based methods have been found to be most favorable for non-contact, non-invasive diagnosis, especially in the case of tissue stiffness analysis. We report here, the fabrication and characterization details of a new contact based transducer system for qualitative determination of the stiffnesses of non-piezoelectric substrates using the phenomenon of Surface Acoustic Waves (SAW). Preliminary trials to study the functionality of this system were carried out on various metallic and non-metallic substrates, and the results were found to be satisfactory. To confirm the suitability of this system for biomedical applications, similar trials have been conducted on tissue mimicking phantoms with varying degrees of stiffness.

并联刨床刚度分析及实验研究

为了提高刨削加工能力,而采用考虑到并联机构的特点而提出了并联刨床的概念并对其进行了简单说明.采用对机床进行分解的方法对机床的各功能模块分别建立刚度模型,并利用变形线性叠加的原理对机床的并联部分刚度进行分析.采用有限元软件对机床的床身框架及平面约束机构部分的刚度进行分析.并以仿真和实验加工的方式进行了刚度特性研究.

3自由度并联柔索驱动变刚度操作臂的刚度控制

利用柔索的弹性及驱动冗余性构造了一种3自由度并联柔索驱动变刚度操作臂,在静力学与刚度分析的基础上,进行刚度控制研究。首先,将柔索驱动力映射到关节空间,并分析等效关节力与柔索张力和外力的关系, 提出该操作臂的三维力矢量闭合原理。根据微分变换原理进行刚度分析,得到关节刚度矩阵及操作手刚度矩阵, 并进行数值算例分析,结果表明:刚度与柔索的张力有关,调节柔索张力可以改变系统刚度。最后,采用位置与张力混合控制的策略,对该变刚度操作臂进行了刚度控制,并进行了仿真验证。

Comparison of 3D finite element analysis derived stiffness and BMD to determine the failure load of the excised proximal femur

Introduction: Bone mineral density (BMD) is currently the preferred surrogate for bone strength in clinical practice. Finite element analysis (FEA) is a computer simulation technique that can predict the deformation of a structure when a load is applied, providing a measure of stiffness (Nmm−1). Finite element analysis of X-ray images (3D-FEXI) is a FEA technique whose analysis is derived froma single 2D radiographic image. Methods: 18 excised human femora had previously been quantitative computed tomography scanned, from which 2D BMD-equivalent radiographic images were derived, and mechanically tested to failure in a stance-loading configuration. A 3D proximal femur shape was generated from each 2D radiographic image and used to construct 3D-FEA models. Results: The coefficient of determination (R2%) to predict failure load was 54.5% for BMD and 80.4% for 3D-FEXI. Conclusions: This ex vivo study demonstrates that 3D-FEXI derived from a conventional 2D radiographic image has the potential to significantly increase the accuracy of failure load assessment of the proximal femur compared with that currently achieved with BMD. This approach may be readily extended to routine clinical BMD images derived by dual energy X-ray absorptiometry. Crown Copyright © 2009 Published by Elsevier Ltd on behalf of IPEM. All rights reserved

Comparison of 3D finite element analysis derived stiffness and BMD to determine the failure load of the excised proximal femur

Bone mineral density (BMD) is currently the preferred surrogate for bone strength in clinical practice. Finite element analysis (FEA) is a computer simulation technique that can predict the deformation of a structure when a load is applied, providing a measure of stiffness (N mm− 1). Finite element analysis of X-ray images (3D-FEXI) is a FEA technique whose analysis is derived from a single 2D radiographic image. This ex-vivo study demonstrates that 3D-FEXI derived from a conventional 2D radiographic image has the potential to significantly increase the accuracy of failure load assessment of the proximal femur compared with that currently achieved with BMD.

Prediction of the stiffness of nanoclay-polypropylene composites using a monte carlo finite element analysis approach

The present work deals with the prediction of stiffness of an Indian nanoclay-reinforced polypropylene composite (that can be termed as a nanocomposite) using a Monte Carlo finite element analysis (FEA) technique. Nanocomposite samples are at first prepared in the laboratory using a torque rheometer for achieving desirable dispersion of nanoclay during master batch preparation followed up with extrusion for the fabrication of tensile test dog-bone specimens. It has been observed through SEM (scanning electron microscopy) images of the prepared nanocomposite containing a given percentage (3–9% by weight) of the considered nanoclay that nanoclay platelets tend to remain in clusters. By ascertaining the average size of these nanoclay clusters from the images mentioned, a planar finite element model is created in which nanoclay groups and polymer matrix are modeled as separate entities assuming a given homogeneous distribution of the nanoclay clusters. Using a Monte Carlo simulation procedure, the distribution of nanoclay is varied randomly in an automated manner in a commercial FEA code, and virtual tensile tests are performed for computing the linear stiffness for each case. Values of computed stiffness modulus of highest frequency for nanocomposites with different nanoclay contents correspond well with the experimentally obtained measures of stiffness establishing the effectiveness of the present approach for further applications.

Coupled foundation-superstructure analysis and influence of building stiffness on foundation response

This paper proposes a simple method to include superstructure stiffness in foundation analyses. The method involves extracting a small "condensed structural matrix" from finite element models of the superstructure, which can then be incorporated into pile group or piled raft analyses using common approaches such as elastic continuum or load transfer methods. The matrix condensation method directly couples structural and geotechnical analyses, and eliminates the need for iterative analyses between structural and geotechnical engineers. Effectiveness of the approach is illustrated through analyses of several buildings designed with a typical floor plan but with varying heights. The parametric study illustrates that superstructure stiffness can have a significant influence on foundation settlement estimates, and the stiffening effects are dominated by the lower stories of the superstructure. The proposed method aims to bridge the gap between structural and geotechnical analyses. Also, being a computationally simple and accurate approach, it is applicable to parametric or optimization studies that would otherwise involve large amounts of analyses. © 2010 ASCE.