•The 450/-450/-450/450 clamped shell with y – stiffener should be preferred.•The shells must have nx = 0, ny = 7 stiffeners below the mid-surface.•The clamped shells must have stiffeners satisfying ...dst/h = 8.•The nonlinear approach for stiffened shells is must to get correct predictions.
The non-dimensional fundamental frequencies and mode shapes of laminated composite singly curved stiffened shells are studied in this paper for varying boundary condition, lamination and stiffener properties like orientations, eccentricities, numbers and depth. An isoparametric C0 continuous finite element code combining von-Karman nonlinearity and Sanders’ first approximation theory is proposed here. The curved surfaces are formulated by nonlinear strains while the stiffeners adopted both geometrically linear and nonlinear strains. Correctness of the proposed approach is confirmed through solutions of benchmark problems. The results are critically discussed, and it is concluded that the clamped 450/-450/-450/450 shell with y - stiffeners (nx = 0, ny = 7) located below the mid-surface shows the greatest fundamental frequencies. This study concludes that the nonlinear approach is essential for both shell and stiffener for correct predictions of natural frequencies and mode shapes. The relatively simpler linear approach can be considered for shells having single x – stiffener only.
The extended finite element method (XFEM) is utilized for high-frequency eddy current analysis. However, when a conductor with a curved surface is involved, the geometric approximation tends to ...degrade due to the coarse mesh used in XFEM. To enhance the approximation accuracy, exact boundary representation (EBR) methods are employed within XFEM for eddy current analysis. The proposed method is validated using a round conductor model, demonstrating a substantial reduction of error in global quantities such as Joule losses compared to conventional methods.
Considering the both effect of boundary approximation and numerical quadrature, a second‐order isoparametric element method is given to solve the homogeneous isotropic plane linear elasticity problem ...in domain Ω with curved boundary. By using technically analysis, the optimal error estimate with ‖u˜→−u→h‖1,Ωh=O(h2) is obtained, where the function u˜→ is an extension of the true solution u→ to Ω˜. It yields better accuracy than traditional quadratic finite element method. Finally, two numerical examples are presented, which further illustrate the analytical result and show the scheme is effective.
The effect of the material property inhomogeneity on the stress concentration factor (SCF) due to a circular hole in functionally graded panels is numerically investigated. The multiple isoparametric ...finite element formulation is used to simulate the elastostatic boundary value problem. A parametric study is performed by varying the functional form and the direction of the material property gradation. The material property inhomogeneity is characterized by the intrinsic inhomogeneity length scale, modulus ratio and the power-law index. The results from our parametric study showed that the SCF is reduced when Young's modulus progressively increased away from the hole. The angular position of the maximum tensile stress on the surface of the hole remains unaffected by the material property inhomogeneity. The SCF is seen to be most influenced by the power-law index, followed by the variation of the inhomogeneity length scale. The SCF is least affected by the modulus ratio.
Recently, application of Cross Laminated Timber (CLT) for medium and high-rise wooden structure is spreading rapidly even in Japan. It has been proposed not only CLT panel structures but also ...structures combined CLT panel with frame members which is used wood-based materials such as Glued Laminated Timber (Glulam) or Laminated Veneer Lumber (LVL) and so on. In a case of CLT is used as wall column and Glulam is used as beam, it is important that appropriate evaluation of deformation property between CLT and Glulam. Wood has strong anisotropy, and material characteristics are completely different when subject to compressive stress in longitudinal direction or direction that perpendicular to the grain. Especially, it is known that stiffness and strength become low value in the case subject to partial compressive strain in direction of perpendicular to the grain. To evaluate deformation property of wooden structures, it is important that transact unique characteristics of wood such as mentioned above properly. In this paper, the yield criterion and strain hardening rule using non-dimensional stresses for orthotropic materials such as wood proposed in previous papers are applied to numerical analysis of CLT-Glulam joint and comparison between result of analysis and experiment are shown. Firstly, partial compression test of glulam is conducted and compared with numerical analysis. It is shown that method for decide material properties for analysis, which is that a certain value is decided from material experiment and other properties are calculated using ratio among material properties of wood proposed in previous studies. From the result of numerical analysis, stiffness and strength have not improved even though increase in size of specimen contrary to expectations. Reason of the above result is expected to effect of inclination of annual rings in the end grain. Accordingly modeling method considering inclination of annual rings in the end grain is proposed and numerical experiment applied the method is performed. From the result of numerical experiment, if effect of inclination of annual rings is not considered, it is confirmed that obtained value from analysis is bigger than experimental value. In the case that width of glulam is 210mm, by the effect of inclination of annual rings, decrease 55% (from 519.05 N/mm2 to 235.59 N/mm2) in Young’s modulus and 22% (from 2.74 N/mm2 to 2.14 N/mm2) in yield stress. Moreover, result of compression test is shown and it is verified that Young’s modulus and yield stress decrease relatively even though size of specimen increase by effect of inclination of annual rings. Finally, based on the above discussions, numerical analysis of partial compression test is conducted once again. The result of analysis is well corresponding to experimental result and appropriateness of the proposed method is confirmed. In the case that width of glulam is 150mm, by adjusting input data for analysis to experimental result, difference between analysis and experiment is only 1% (analysis: 701.26 N/mm2, experiment: 711.05 N/mm2) in Young’s modulus and 6% (analysis: 3.73 N/mm2, experiment: 3.96 N/mm2) in yield stress. It is clarified that whether considering inclination of annual rings in the end grain or not have great effect on result of numerical analysis. According to the result, effect of inclination of annual rings would be remarkable if width of glulam become larger and a part which annual rings inclining become wider.
•External circumferential crack problem of superconducting cylinder is investigated.•A functionally graded superconducting cylinder is analyzed.•The magnetically impermeable crack surface condition ...is applied.•The generalized Irie-Yamafuji critical state model outside the crack region is adopted.
In this study, the multiple isoparametric finite element method (MIFEM) is used to investigate external circumferential crack problem of a functionally graded superconducting cylinder subjected to electromagnetic forces. The superconducting cylinder is composed by Bi2223/Ag composite with material parameters varying. A crack reference region is defined to reflect the effects of crack on flux and current densities, and the magnetically impermeable crack surface condition and the generalized Irie–Yamafuji critical state model outside the crack region are adopted. The distributions of magnetic flux density in the superconducting cylinder are obtained analytically for both the zero-field cooling (ZFC) and the field cooling (FC) activation processes. Based on the MIFEM, the stress intensity factors (SIFs) at crack fronts in the process of field ascent and/or descent are then numerically calculated. It is interesting to note from numerical results that for the present crack model in the ZFC activation process, the crack is easily propagate and grow with the applied field increases, and that in the field descent process of either the ZFC case or FC case, the crack generally does not propagate. In addition, in the field ascent process of the ZFC case, the SIFs depend on not only the crack depths and model parameters but also the applied field. The present study should be helpful to the design and application of high-temperature superconductors with external edge cracks.
The near-tip variable-separable singular series solution around a stationary crack embedded in plastically graded materials is derived and complementary modified-boundary-layer finite element ...simulations are performed. The stationary crack is subjected to an anti-plane shear (mode-3 or torsion) loading and the material nonlinearity is characterized by a power-law hardening model. The spatial variation of the material property (yield-stress) is allowed to be in any arbitrary direction around the crack and is characterized by another power-law form. The complementary modified-boundary-layer finite element simulations are performed using the newly developed nonlinear multiple-isoparametric finite element formulation. Our full-field finite element simulations validate the existence of the variable-separable form of solution. Our analysis and simulations predict that the most-singular term in the series solution remains unaffected by the inhomogeneity and its direction. The second-singular term of the series solution is however affected by the inhomogeneity and its direction. The second-term dominant region depends on the directionality of the inhomogeneity and is maximum for the
x-gradation and minimum for the
y-gradation. The contribution of the second-term is significant and hence a two-term based fracture mechanics methodology is required in designs using plastically graded materials.
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