Tetsuya Tsujikami

Cost effective design procedure for laminated composite structure based on GA

We present a design procedure for symmetrically laminated composite structure with GA (Genetic Algorithm) and finite element analysis. Design variables to enhance the rigidity of the laminated composite structure are the number of laminae, the fiber orientation and the stacking sequence. Here, the fiber orientation is selected among some prepared angles from a manufacturing viewpoint. In a conventional design procedure based on GA an objective function is calculated by costly finite element analysis. Consequently, it is quite time consuming and unpractical. In this paper, to minimize the displacement at a point in the structure, we define an approximated rigidity function of the laminated composites by means of weighing coefficients and transformed elastic moduli in the prepared angles. The weighing coefficients are initially determined using the distribution of principal stress in the structure under an applied load. Then, we can guess that reinforcements should be oriented according to the weighing coefficients with which the rigidity function takes maximum. To find the global optimum solution, the weighing coefficients are adjusted with as small a number of finite element analyses as possible. As a conclusion, the proposed procedure can reduce the computational cost remarkably compared to the conventional one, and can be applied practically to arbitrary shaped structures.

Estimation of Changes in Mechanical Bone Quality by Multi-scale Analysis with Remodeling Simulation

Mechanical bone quality and its related load-supporting function at the macro-scale is a result of adaptation, which is achieved by trabecular bone remodeling at the microscale. The increase in fracture risk in patients with osteoporosis is a clear example of this structure/function relationship, where decreased bone mass as a result of structural changes during remodeling leads to changes in the stress distribution of trabecular bone. This stress distribution is closely associated with the morphology and orientation of the nano-scale biological apatite (BAp) crystallite - the main factor determining bone quality. It is therefore important to evaluate both the changes in mechanical bone quality and bone mass when predicting fracture risk. We propose a computational model of remodeling and multi-scale stress analysis of trabecular bone based on homogenization techniques, considering the mechanical properties of the BAp crystallite orientation to be anisotropic. We first identified morphological changes in healthy and osteoporotic cases, and then performed a multi-scale stress analysis for the remodeled osteoporotic trabecular bone to elucidate changes in mechanical bone quality leading to fracture risk. Our results demonstrate that the load-supporting function of remodeled bone correlates with mechanical adaptability to external loads through remodeling, despite a progressive decrease in bone mass. These findings suggest the potential to use changes in mechanical bone quality as a predictor of fracture risk. The availability of these simulation methods for bone quality evaluation is discussed.

REMODELING SIMULATION ESTIMATES CHANGES IN MECHANICAL PROPERTIES OF OSTEOPOROTIC BONES

Osteoporosis causes bone fracture due to changes in the stress distribution of the trabecular bone with structural change as well as a decrease in bone mass. It arises from an imbalance in bone remodeling which involves the coupling of bone formation and resorption by osteoblast/osteoclast [Cowin SC, 1991]. Therefore, an evaluation of mechanical properties of the trabecular bone with its morphological change by remodeling is necessary to estimate the long-term fracture risk. In this study, we simulated bone remodeling of a pig trabecular bone model and estimated morphology of healthy and osteoporotic cases using our proposed mathematical model of bone remodeling [Adachi T, 2001]. We also evaluated fracture risks using a cumulative histogram of high stress. Potential of evaluation of change in mechanical properties of the trabecular bone considering its remodeling is discussed.

Proposal Regarding Analytical Technique of Mechanical Behavior for Textile Composites by Inclusion Element Method

As one of the analytical technique of mechanical behavior for the textile composites, inclusion element method by the subcell division was proposed, and the verification on the effectiveness was carried out. In the inclusion element method, it is possible to analyze using very simple grid finite element, obtaining the element siffiness by the inclusion method by cooperation with the fabric structure simulator. As a result of comparing with the real model analysis, it was shown that peculiar condition of the woven composites in the deformation behavior is confirmed and the internal stress is also estimable. The analytical result by the inclusion element model is greatly dependent on approach to division of the subcell, but if it is same or lower level number of elements as the real model, it was shown that the sufficient result was obtained.

Fatigue. Fatigue Crack Propagation Paths Across the Interface of Macroscopic Hardness Discontinuity in Material.

The criterion determining the fatigue crack propagation path near or across the interface of hardness discontinuity in material inhomogeneous with respect to hardness was experimentally investigated. The Δδθ maximum criterion was used as a reference. Single-edge-cracked panels of S45C hard steel subjected to uniform pulsating axial stresses of R=0.1 were used as test specimens, which had in each a partial slant band-like or circular area hardened by induction-heat-treatment; the fatigue cracks were intended to propagate perpendicular to the specimen axis, if the Δδθ maximum criterion was valid. It was observed that the fatigue cracks propagated in all cases straight and perpendicularly to the specimen axis, crossing the interface of the hardness discontinuity, indicating that the Δδθ maximum criterion was valid in this case.

SUGGESTION OF ANALYTICAL METHOD OF THREE-DIMENSIONAL STRESS ANALYSIS FOR LAMINATED COMPOSITE STRUCTURES

It is well known that the mechanical properties of laminated composites depend on the stacking sequences. As the bending modulus of elasticity is affected remarkably by the stacking sequences, the stress and strain analyses for laminated composite structure require a special technique. Therefore, a new analytical method has been proposed in order to calculate the mechanical behaviour of laminated structures in this paper. The proposed method has been applied for a laminated composite structure as a numerical example. As a result, it has been recognized that the numerical behaviour of the composite structure with anisotropic properties under mixed loads of bending and tension can be analyzed by the proposed method, even if it has two different moduli of elasticity of bending and tension. In addition, CPU time of FEM based on the proposed method can be reduced remarkably as compared with ordinary FEM.

Development of personal computer program of stress analysis for composite meterials.

It has become now possible to analyze by a personal computer even complicated problems with required a large sized computer before, because of remarkable development of personal computers.In the present study, the personal computer program of F.E.M. by triangular elements has been developed in order to analyze the stresses in composite materials. It is shown that the mechanical behavior of composite materials can be analyzed by the developed computer program. As the accuracy of analysis by triangular elements depends strongly on the number of nodes and elements, the program by isoparametric elements which have good accuracy of calculations has been also developed. And the formulation has been evaluated by the comparison between theoretical value and calculational one under bending conditions of isotropic and anisotropic plates. In case of stress analysis for isotropic materials by isoparametric elements, the computational results were in good agreement with the theoretical ones. In case of triangular elements, the computational results agreed with the theoretical ones when the number of nodes was more than 150. The stress analysis for anisotropic materials, however, the computational results by both isoparametric and triangular elements were similar. Therefore, the F.E.M. by triangular elements is considered reasonable for composite materials.The pre- and post-processing programs utilizing the graphics capabilities of the personal computer have been also developed. As the results of the present study, it is recognized that the developed personal computer program is very useful for structure design of composite materials.

A method of fatigue life prediction for composite materials. In case of prediction based on the extension mode.

In this paper, a fatigue life prediction method based on linear fracture mechanics is proposed to composite materials. In order to evaluate this method, the cyclic loading tests of graphite/epoxy composites plates with [±30]s, [±45]s and [±60]s laminate orientations were carried out.It was revealed that the computational result was satisfactory agreement with the experimental ones except long life region [±30]s laminate orientations. The fracture mode was the combination of tension and shear modes when the angle between loading direction and fiber orientation became small. Therefore, it is recognized that the long life prediction of these materials has to require fracture mechanics base on the combined mode which is not dealt with in this paper.Furthermore, the effects of material properties on fatigue life were investigated as an application of the proposed model to material design. As a result, it became clear that the fatigue life is affected by the ultimate tensile and shear strengths of the matrix and depends strongly on the influence of initial crack length that is calculated from the size of voids or defects.