Finite element analysis using interfragmentary strain theory for the fracture healing process to which composite bone plates are applied

The present paper deals with finite element analyses to estimate the healing efficiency of fractured long bones to which various composite bone plates are applied. To estimate the callus modulus according to the healing period, interfragmentary strain theory was used, and the iterative process for updating the newly determined callus properties in every finite element was implemented by a user-defined sub-routine constructed by the Python code. The results of analysis revealed that a composite bone plate made of a plain weave carbon/epoxy composite whose Young’s modulus was in the range of 30–70 GPa produced a positive effect on the healing efficiency relieving stress-shielding effect. This result can be used in the detailed design of high-performing composite bone plates to determine more effective shapes and stacking sequences for better healing efficiency.     

Postbuckling behavior of face/core debonded composite sandwich plate considering matrix crack and contact effect

A study of postbuckling behavior in face/core interface debonded composite sandwich plates is presented. A methodology is proposed for simulating the multi-failure responses, such as initial and postbuckling, contact of interfacial debonding front region and face matrix cracking, etc. A finite element postbuckling analysis is conducted on the basis of the Von Karman nonlinearity assumption and the zig–zag deformation theory combined with a debonding model and a multi-scalar damage model. The numerical models and methods are briefly introduced in this paper and some numerical examples are presented to illustrate it. From numerical results and discussion, it is clear that the effects of matrix cracking damage and contact upon postbuckling behavior of the debonded composite sandwich plates are significant during compressive loading process. The method and numerical conclusion provided in this paper should of great value to engineers dealing with composite sandwich structures.     

Free vibration and buckling analysis of laminated composite plates using the NURBS-based isogeometric finite element method

An isogeometric finite element method based on non-uniform rational B-splines (NURBS) basis functions is developed for natural frequencies and buckling analysis of thin symmetrically laminated composite plates based upon the classical plate theory (CPT). The approximation of the solution space for the deflection field of the plate and the parameterization of the geometry are performed using NURBS-based approach. The essential boundary conditions are formulated separately from the discrete system equations by the aid of Lagrange multiplier method, while an orthogonal transformation technique is also applied to impose the essential boundary conditions in the discrete eigen-value equation. The accuracy and the efficiency of the proposed method are thus demonstrated through a series of numerical experiments of laminated composite plates with different boundary conditions, fiber orientations, lay-up number, eigen-modes, etc. The obtained numerical results are then compared with either the analytical solutions or other available numerical methods, and excellent agreements are found.     

Fatigue life prediction of a rubber mount based on test of material properties and finite element analysis

Failure analysis and fatigue life prediction are very important in the design procedure to assure the safety and reliability of rubber components. The fatigue life of a rubber mount was predicted by combining test of material properties and finite element analysis (FEA). The natural rubber material material’s fatigue life equation was acquired based on uniaxial tensile test and fatigue life tests of the natural rubber. The strain distribution contours and the maximum total principal strains of the rubber mount at different loads in the x and y directions were obtained using finite element analysis method. The critical region cracks prone to arise were obtained and analyzed. Then the maximum total principal strain was used as the fatigue parameter, which was substituted into the natural rubber’s fatigue life equation, to predict the fatigue life of the rubber mount. Finally, fatigue lives of the rubber mount at different loads were measured on a fatigue test rig to validate the accuracy of the fatigue life prediction method. The test results imply that the fatigue lives predicted agree well with the test results.     

An accurate higher-order theory and C finite element for free vibration analysis of laminated composite and sandwich plates

At present, it is difficult to accurately predict natural frequencies of sandwich plates with soft core by using the C⁰ plate bending elements. Thus, the C¹ plate bending elements have to be employed to predict accurately dynamic response of such structures. This paper proposes an accurate higher-order C⁰ theory which is very different from other published higher-order theory satisfying the interlaminar stress continuity, as the first derivative of transverse displacement has been taken out from the in-plane displacement fields of the present theory. Therefore, the C⁰ interpolation functions is only required during its finite element implementation. Based on the Hamilton’s principle and Navier’s technique, analytical solutions to the natural frequency analysis of simply-supported laminated plates have been presented. To further extend the ranges of application of the proposed theory, an eight-node C⁰ continuous isoparametric element is used to model the proposed theory. Numerical results show the present C⁰ finite element can accurately predict the natural frequencies of sandwich plate with soft core, whereas other global higher-order theories are unsuitable for free vibration analysis of such soft-core structures.     

SectionBuilder: An innovative finite element tool for analysis and design of composite rotor blade cross-sections

SectionBuilder is a finite element based tool for analysis and design of composite rotor blade cross-sections. The tool can create the cross-sections with parametric shapes and arbitrary configurations. It has the ability to generate single- and multi-cell cross-sections with arbitrary lay-ups where the material properties for each layer can be defined on the basis of the design requirements. It can create the variation of thickness of skin and D-spars for rotor blades by considering ply drops. Cross-sections are often reinforced by core material for constructing realistic rotor blade cross-sections. The tool has the ability to integrate core materials into the cross-sections. After meshing the cross-section, the tool determines the sectional properties using finite element analysis. This tool computes sectional properties including stiffness matrix, compliance matrix, mass matrix, and principal axes. A visualization environment is integrated with the tool for visualizing the stress and strain distributions over the cross-section. The detail about the development steps and application of SectionBuilder is presented in this paper.     

Dynamic analysis of laminated composite plates traversed by a moving mass based on a first-order theory

The dynamic response of angle-ply laminated composite plates traversed by a moving mass or a moving force is investigated. For this purpose, a finite element method based on the first-order shear deformation theory is used. Stationary and adaptive mesh techniques have been applied as two different meshing schemes. The adaptive mesh strategy is then used to avoid off-nodal position of moving mass. In this manner, the finite element mesh is continuously adapted to follow and comply with the path of moving mass. A Newmark direct integration method is employed to solve the equations of motion. Parametric study is directed to find out how different parameters like mass of the moving object as well as the type of the angle-ply laminated composite plates affect the dynamic response. Numerical results show the significant effects of the stacking order on the dynamic responses of the composite structures under a moving mass. It is found that although [30/−60/−60/30] lamination shows the highest maximum vertical deflection but [−45/45/45/−45] lamination has the highest value of the dynamic amplification factor. The dynamic amplification factor for different stacking orders and mass velocities is less than 1.25.     

The finite element analysis of composite laminates and shell structures subjected to low velocity impact

In this investigation, the composite laminate and shell structures subjected to low velocity impact are studied by the ANSYS/LS-DYNA finite element software. The contact force is calculated by the modified Hertz contact law in conjunction with the loading and unloading processes. In the case of composite laminate, the impact-induced damage including matrix cracking and delamination are predicted by the appropriated failure criteria and the damaged area are plotted. Two types of shell structure, cylindrical and spherical shells, are considered in this paper. The effects of various parameters, such as shell curvature, clamped or simple supported boundary conditions and impactor velocity are examined through the parametric study. Numerical results show that structures with greater stiffness, such as smaller curvature and clamped boundary condition, result to a larger contact force and a smaller deflection. The impact response of the structure is proportional to the impactor velocity.     

Evaluation of interphase properties in a cellulose fiber-reinforced polypropylene composite by nanoindentation and finite element analysis

The hardness and elastic modulus of the cellulose fiber and polypropylene (PP) matrix in a cellulose fiber-reinforced PP composite were investigated by nanoindentation with a continuous stiffness technique. Nanoindentation with different indentation depths and spacings was conducted to measure hardness and elastic modulus in the interphase region, which was modified by maleic anhydride-grafted PP and γ-amino propyltrimethoxy silane (γ-APS) sizing. A line of indents was produced from the fiber to the matrix. There was a gradient of hardness and modulus across the interphase region. The distinct properties of the transition zone were revealed by 1–4 indents, depending on nanoindentation depth and spacing. Based on the results of nanoindentation, it was assumed that the width of the property transition zone is less than 1 μm. However, three dimensional finite element analysis shows that even a perfect interface without property transition has almost same interphase width as that measured by nanoindentation. Using existing nanoindentation techniques, it will be difficult to calculate exact mechanical properties without the effect of neighboring material property in at least 8 times smaller region than indent size.     

Experimental and finite element analysis of a double strap joint between steel plates and normal modulus CFRP

Strengthening of steel structures using externally-bonded carbon fibre reinforced polymers ‘CFRP’ is a rapidly developing technique. This paper describes the behaviour of axially loaded flat steel plates strengthened using carbon fibre reinforced polymer sheets. Two steel plates were joined together with adhesive and followed by the application of carbon fibre sheet double strap joint with different bond lengths. The behaviour of the specimens was further investigated by using nonlinear finite element analysis to predict the failure modes and load capacity. In this study, bond failure is the dominant failure mode for normal modulus (240 GPa) CFRP bonding which closely matched the results of finite elements. The predicted ultimate loads from the FE analysis are found to be in good agreement with experimental values.     

Free and forced vibration analysis of laminated composite plates and shells using a 9-node assumed strain shell element

The natural frequencies of isotropic and composite laminates are presented. The forced vibration analysis of laminated composite plates and shells subjected to arbitrary loading is investigated. In order to overcome membrane and shear locking phenomena, the assumed natural strain method is used. To develop a laminated shell element for free and forced vibration analysis, the equivalent constitutive equation that makes the computation of composite structures efficient was applied. The Mindlin-Reissner theory which allows the shear deformation and rotary inertia effect to be considered is adopted for development of nine-node assumed strain shell element. The present shell element offers significant advantages since it consistently uses the natural co-ordinate system. Results of the present theory show good agreement with the 3-D elasticity and analytical solutions. In addition the effect of damping is investigated on the forced vibration analysis of laminated composite plates and shells.     

Linear and Geometrically nonlinear analysis of plates and shells by a new refined non-conforming triangular plate/shell element

A refined non-conforming triangular plate/shell element for linear and geometrically nonlinear analysis of plates and shells is developed in this paper based on the refined non-conforming element method (RNEM). A conforming triangle membrane element with drilling degrees of freedom in Cartesian coordinates and the refined non-conforming triangular plate-bending element RT9, in which Kirchhoff kinematic assumption was adopted, are used to construct the present element. The displacement continuity condition along the interelement boundary is satisfied in an average sense for plate analysis, and the coupled displacement continuity requirement at the interelement is satisfied in an average sense, thereby improving the performance of the element for shell analysis. Selectively reduced integration with stabilization scheme is employed in this paper to avoid membrane locking. Numerical examples demonstrate that the present element behaves quite satisfactorily either for the linear analysis of plate bending problems and plane problems or for the geometrically nonlinear analysis of thin plates and shells with large displacement, moderate rotation but small strain.