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.
A finite element method is developed for simulating frequency domain electromagnetic responses due to a dipole source in the 2-D conductive structures. Computing costs are considerably minimized by ...reducing the full three-dimensional problem to a series of two-dimensional problems. This is accomplished by transforming the problem into y-wave number （Ky） domain using Fourier transform and the y-axis is parallel to the structural strike. In the Ky domain, two coupled partial differential equations for magnetic field Hy and electric field Ey are derived. For a specific value of Ky, the coupled equations are solved by the finite element method with isoparametric elements in the x-z plane. Application of the inverse Fourier transform to the Ky, domain provides the electric and magnetic fields in real space. The equations derived can be applied to general complex two-dimensional structures containing either electric or magnetic dipole source in any direction. In the modeling of the electromagnetic measurement, we adopted a pseudo-delta function to distribute the dipole source current and circumvent the problem of singularity at the source point. Moreover, the suggested method used isoparametric finite elements to accommodate the complex subsurface formation. For the large scale linear system derived from the discretization of the Maxwell＇s equations, several iterative solvers were used and compared to select the optimal one. A quantitative test of accuracy was presented which compared the finite element results with analytic solutions for a dipole source in homogeneous space for different ranges and different wave numbers Ky. to validate the addressed the effects of the distribution range τ of the homogeneous medium. code and check its effectiveness. In addition, we pseudo-delta function on the numerical results in
The main aim of this paper is to show that the quadrilateral mesh condition RDP(N, ψ) is only sufficient but not necessary for the optimal order error estimate of the Q₁ isoparametric element in the ...H¹ norm.
New and available isoparametric finite elements having the option function on nodes are developed. It is shown that the option function on nodes leads to the more adaptable and applicable tool in ...generation of finite element meshes. According to the standard finite element procedure, new 2D- and 3D- isoparametric finite elements are formulated. Also, the availability and applicability of the present approach are, with aid of several numerical examples, discussed and examined.
Extended isoparametric finite method (XIFEM) consists in enriching the basis of the classical finite element method and taking into account the discontinuity of the displacement field across the ...crack by a discontinuous function along the crack line. It simulates the discontinuous character resulted from discontinuity such as crack or joint and by some trigonometric basis functions around the crack tip to embody singularity at the end of discontinuity. With the improved XIFEM, the tracking of crack propagation in reinforced concrete beams strengthened with FRP is simulated and the failure model is analyzed. Compared with the traditional finite element method, the XIFEM allows crack surface to be in any position of finite element mesh without dense mesh near the crack tips and without re-meshing, therefore crack growth is traced and modeled effectively. The results show the effectiveness and superiority of the improved XIFEM.
Considering the combined effect of boundary approximation and numerical integration, error estimates for the isoparametric mixed finite element solution of fourth order elliptic problems with ...variable coefficients in convex domains, which, in the particular case of aniso-/ortho-/ isotropic plate bending problems, gives a direct and simultaneous approximation to bending moment tensor field Ψ=(ψij)1≤i,j≤2 and displacement field `u', have been developed. Results of numerical experiments justify the theoretical results.
In this paper torsion of prismatic bars considering elastic–plastic material behaviour is studied. Based on the presented variational formulation associated isoparametric finite elements are ...developed. The unknown warping function is approximated using an isoparametric concept. The elastic–plastic stresses are obtained by an exact integration of the rate equations. Thus the ultimate torque can be calculated in one single load step. This quantity describes the plastic reserve of a bar subjected to torsion. Furthermore, for linear isotropic hardening no local iterations are necessary to compute the stresses at the integration points. The numerical results are in very good agreement with available analytical solutions for simple geometric shapes. The arbitrary shaped domains may be simply or multiple connected.
New and available isoparametric finite elements having the option function on nodes are developed. It is shown that the option function on nodes leads to the more adaptable and applicable tool in ...generation of finite element meshes. According to the standard finite element procedure, new 2D- and 3D- isoparametric finite elements are formulated. Also, the availability and applicability of the present approach are, with aid of several numerical examples, discussed and examined.
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