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The paper presents the features of solutions to nonlocal elasticity problems in domains with stepped transitions and elliptical notches. A comparative analysis of the solutions obtained in the classical and nonlocal elasticity theories was carried out, as well as an analysis of the influence of the main parameters of the model on the final results. The presented solutions for the region with a step transition are in qualitative agreement with the experimental data and have similar portraits of deformations and resultant stresses along the loading axis. In regions with elliptical notches, similar effects are observed. In addition to qualitative agreement with experiments, solutions in the nonlocal formulation have lower stress values in the concentrators and exhibit edge effects, which are characterized by sharp stress and strain gradients at the domain boundaries. The solutions were carried out numerically by the finite element method. [ABSTRACT FROM AUTHOR]

ABSTRACT Aimed primarily for educational use, an effective platform for 2-dimensional FE stress analysis was developed by making use of the Excel-VBA program. With the undergraduate students as the target group, the educational emphasis was placed on the practical application of linear elasticity and the proper use of the FE method. As a part of the project, the students were requested to solve a stress concentration problem by conducting mesh convergence study using Excel-VBA functionality. They generated the mesh manually by drawing the figures on the grid-paper. This time consuming experience is usually sufficiently memorable to provide the student with the sense of the required mesh size for proper FE analysis. In addition, the use of tabular data in Excel allows the students to easily conduct the FE analysis. Further, the reports by students clearly manifest that the reliability of the FE method is highly dependent on the experience and the theoretical knowledge of the engineer. In sum, Excel-VBA is a highly efficient tool for introducing the FE method and can motivate the students to study this subject further. © 2017 Wiley Periodicals, Inc. Comput Appl Eng Educ 25:311-319, 2017; View this article online at ; DOI [ABSTRACT FROM AUTHOR]

Summary: In this paper, we propose a stress recovery procedure for low‐order finite elements in 3D. For each finite element, the recovered stress field is obtained by satisfying equilibrium in an average sense and by projecting the directly calculated stress field onto a conveniently chosen space. Compared with existing recovery techniques, the current procedure gives more accurate stress fields, is simpler to implement, and can be applied to different types of elements without further modification. We demonstrate, through a set of examples in linear elasticity, that the recovered stresses converge at a higher rate than that of directly calculated stresses and that, in some cases, the rate of convergence is the same as that of the displacement field. [ABSTRACT FROM AUTHOR]

The scaled boundary radial point interpolation method (SBRPIM), a new semi-analytical technique, is introduced and applied to the analysis of the stress-strain problems. The proposed method combines the advantages of the scaled boundary finite element method and the boundary radial point interpolation method. In this method, no mesh is required, nodes are scattered only on the boundary of the domain, no fundamental solution is required, and as the shape functions constructed based on the radial point interpolation method possess the Kronecker delta function property, the boundary conditions of problems can be imposed accurately without additional efforts. The main ideas of the SBRPIM are introducing a new method based on boundary scattered nodes without the need to element connectivity information, satisfying Kronecker delta function property, and being capable to handle singular problems. The equations of the SBRPIM in stress-strain fields are outlined in this paper. Several benchmark examples of 2-D elastostatic are analyzed to validate the accuracy and efficiency of the proposed method. It is found that the SBRPIM is very easy to implement and the obtained results of the proposed method show a very good agreement with the analytical solution. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents materials and core/shell architectures that provide optimized mechanical properties in packages for stretchable electronic systems. Detailed experimental and theoretical studies quantitatively connect the geometries and elastic properties of the constituent materials to the overall mechanical responses of the integrated systems, with a focus on interfacial stresses, effective modulus, and maximum extent of elongation. Specific results include core/shell designs that lead to peak values of the shear and normal stresses on the skin that remain less than 10 kPa even for applied strains of up to 20%, thereby inducing minimal somatosensory perception of the device on the human skin. Additional, strain-limiting mesh structures embedded in the shell improve mechanical robustness by protecting the active components from strains that would otherwise exceed the fracture point. Demonstrations in precommercial stretchable electronic systems illustrate the utility of these concepts. [ABSTRACT FROM AUTHOR]

SUMMARY The mapping method was introduced in Jeong et al. (2013) for highly accurate isogeometric analysis (IGA) of elliptic boundary value problems containing singularities. The mapping method is concerned with constructions of novel geometrical mappings by which push-forwards of B-splines from the parameter space into the physical space generate singular functions that resemble the singularities. In other words, the pullback of the singularity into the parameter space by the novel geometrical mapping (a non-uniform rational basis spline (NURBS) surface mapping) becomes highly smooth. One of the merits of IGA is that it uses NURBS functions employed in designs for the finite element analysis. However, push-forwards of rational NURBS may not be able to generate singular functions. Moreover, the mapping method is effective for neither the k-refinement nor the h-refinement. In this paper, highly accurate stress analysis of elastic domains with cracks and ∕ or corners are achieved by enriched IGA, in which push-forwards of NURBS via the design mapping are combined with push-forwards of B-splines via the novel geometrical mapping (the mapping technique). In a similar spirit of X-FEM (or GFEM), we propose three enrichment approaches: enriched IGA for corners, enriched IGA for cracks, and partition of unity IGA for cracks. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

An over-deterministic method has been employed for calculating the stress intensity factors (SIFs) as well as the coefficients of the higher-order terms in the Williams series expansions in cracked bodies, using the conventional finite element analysis. For a large number of nodes around the crack tip, an over-determined set of simultaneous linear equations is obtained, and using the fundamental concepts of the least-squares method, the coefficients of the Williams expansion can be calculated for pure mode I, pure mode II and mixed mode I/II conditions. A convergence study has been conducted to examine the effects of the number of nodes used, the number of terms in Williams expansion and the distance of the selected nodes from the crack tip, on the accuracy of the results. It is shown that the simple method presented in this paper, yields accurate results even for coarse finite element meshes or in the absence of singular elements. The accuracy of SIFs and the coefficients of higher-order terms are validated by using the available results in the literature. [ABSTRACT FROM AUTHOR]

The paper presents an expression useful to estimate the notch stress intensity factor (NSIF) from finite element analyses carried out by using a mesh pattern with a constant element size. The evaluation of the NSIF from a numerical analysis of the local stress field usually requires very refined meshes and then large computational effort. The usefulness of the presented expression is that (i) only the elastic peak stress numerically evaluated at the V-notch tip is needed and no longer the whole stress–distance set of data; (ii) the adopted meshes are rather coarse if compared to those necessary for the evaluation of the whole local stress field. The proposed expression needs the evaluation of a virtual V-notch tip radius, i.e. the radius which would produce the same elastic peak stress than that calculated by FEM at the sharp V-notch tip by means of a given mesh pattern. Once such a radius has been theoretically determined for a given geometry, the expression can be applied in a wide range of notch depths and opening angles. [ABSTRACT FROM AUTHOR]

On the basis of detailed three-dimensional (3D) elastic finite element (FE) analyses, this paper provides tractable approximations for elastic T stress solutions for circumferential inner-surface cracks in cylinders. Internal pressure and global bending moment were considered. The FE model and analysis procedure employed in the analysis were verified using existing solutions for both elastic stress intensity factor and T stress. To cover a practical range, three different values of the ratio of the mean radius of cylinder to the thickness, Rm/ t, were selected; furthermore, four different values of the ratio of the crack depth to the thickness, a/ t, ranging from 0.1 to 0.75 and three different values of θ/π ranging from 0.1 to 0.4 were selected. On the basis of FE analyses results, polynomial approximations were proposed at three different locations: surface point, middle point and deepest point. On the basis of the detailed 3D elastic FE analysis, the solutions presented are believed to be the most accurate, and thus provide valuable information for structural integrity assessment considering a crack-tip constraint. [ABSTRACT FROM AUTHOR]

The interest in using fibre-reinforced composites in structural components is increasing. Some of these structural composites, such as wind turbine blades, aircraft components and torsion shafts are subject to fatigue loadings. It is widely accepted that fully reversed cyclic loading is the most adverse loading for fibre-reinforced composites, but the modelling of the material behaviour under this loading condition is very difficult. In this paper, a damage model is presented for woven glass fibre-reinforced composites subject to fully reversed cyclic loading. First fatigue experiments have been conducted in displacement-controlled fully reversed bending and the stiffness degradation and damage patterns have been observed. Based on these experimental data, a damage model has been developed, which includes the in-plane stress components and the degradation of the in-plane elastic properties. The model has been implemented in a commercial finite-element code and simulation of the successive stages in the fatigue life has been performed. The model has been validated for a plain woven glass fabric reinforced composite and simulated stiffness degradation, damage growth and damage distribution have been compared with experimental data. [ABSTRACT FROM AUTHOR]

The article presents a finite element mapping procedure for the coordinate change via higher‐order derivatives to compute the fundamental matrices of laminated thin plates with arbitrary domains in gradient elasticity. In this context, the approximate solution requires Hermite interpolating functions. Therefore, conforming and nonconforming formulations are needed for both membrane and bending degrees of freedom, which require respectively C1$$ {C}^1 $$ and C2$$ {C}^2 $$ continuity. The aim of the current procedure is the possibility to remove the limitations related to the regular rectangular shape which typically characterizes this kind of elements and to introduce arbitrary distortions, discussing the influence of structured and unstructured meshes. The accuracy and convergence features of the methodology are presented through some numerical tests and compared to relevant literature. [ABSTRACT FROM AUTHOR]

Dynamic problems of active optimal vibration control of elastic structures are solved by applying ‘static’ beam elements from standard structural FEM software. The approach uses an analogy between the optimality equations for the vibration control problem and the equations for the static bending of certain beams. The computer implementation of the analogy, which was presented in Part I of the paper, is discussed here in detail. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper discusses an iterative scheme for solving large-scale three-dimensional linear elasticity problems, discretized on a tensor product of two-dimensional and one-dimensional meshes. A framework is chosen of the additive AMLI method to develop a preconditioner of a ‘black-box’ type which is robust with respect to discontinuities of the problem coefficients and imposes only weak (and acceptable in practice) restrictions on the choice of the meshing procedure. The preconditioner works on a hierarchical sequence of nested finite element spaces to solve the problem with arithmetic cost, nearly proportional to the number of degrees of freedom on the finest mesh. It is particularly well suited for the case when the solution is known to be strongly varying in certain subregions of the domain and the mesh is locally prerefined there to reduce the discretization error. Copyright © 1999 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This is a presentation of a quadrilateral finite element for wrinkled curved elastic membranes. A modified form of the deformation gradient enables us to avoid the spurious compressive stresses generated by a classical model. It results in non-linear relations for the eigeneomponents of the Cauchy stres.'; tensor. which are solved by means of a secant method. The application of the element to sail design is presented in this paper. [ABSTRACT FROM AUTHOR]

Mindlin-type plate and shell finite elements are the most widely used ones in the analysis of laminated composite structures. In the commercially available finite element programs, the transverse shear correction factors for these elements are usually the same as for structures made of isotropic materials. In the paper the shear correction factors are determined using energy principles for general laminates in cylindrical bending. Results for various materials and laminates are presented. [ABSTRACT FROM AUTHOR]

The paper reports some numerical experiments on the effectivity of the Zienkiewicz-Zhu error estimate (1987) and comparisons of two adaptive mesh generators: ADMESH, developed by Jin and Wiberg (1990) and MAD2D by Peraire et al. (1987) and Zhu et al. (1990-91). From the experiments we observe that: (1) without any empirical correction, the effectivity of the error estimate for linear triangular elements is good if post-processed continuous stresses are obtained by adequately using an iterative stress recovery procedure (Zienkiewicz et al., 1985), and is also acceptable by using a simple `averaging' procedure; (2) these two mesh generators are basically comparable. [ABSTRACT FROM AUTHOR]

A stiff tubular cellular structure topology is designed by alternatively indenting rectangular contour patterns on the cell ribs. Modified topologies can be obtained by tailoring the geometric parameters. The Poisson's ratios and elastic moduli of the proposed tubular structures with various geometric parameters are determined using finite element method (FEM). Results show that the minimum Poisson's ratio of the proposed structures can reach −0.28. The unit cell topology and orientation can significantly affect the structures deformation behaviors. The structures exhibit mixed mode of bending‐ and stretching‐dominated deformation responses, and show improved specific elastic moduli compared with traditional open‐cell stochastic foams with positive Poisson's ratios. 3D‐printed samples with identical geometric variables to those of the FE models are fabricated, and their Poisson's ratios and stress–strain relationships are determined experimentally, and compared with simulation results. Excellent agreement is achieved between measurements and simulations. The design concept proposed here can be optimized for specific applications via geometric parameters manipulation. [ABSTRACT FROM AUTHOR]

Summary: Within the framework of the displacement‐based virtual element method (VEM), namely, for plane elasticity, an important topic is the development of optimal techniques for the evaluation of the stress field. In fact, in the classical VEM formulation, the same projection operator used to approximate the strain field (and then evaluate the stiffness matrix) is employed to recover, via constitutive law, the stress field. Considering a first‐order formulation, strains are locally mapped onto constant functions, and stresses are piecewise constant. However, the virtual displacements might engender more complex strain fields for polygons, which are not triangles. This leads to an undesirable loss of information with respect to the underlying virtual stress field. The recovery by compatibility in patches, originally proposed for finite element schemes, is here extended to VEM, aiming at mitigating such an effect. Stresses are recovered by minimizing the complementary energy of patches of elements over an assumed set of equilibrated stress modes. The procedure is simple, efficient, and can be readily implemented in existing codes. Numerical tests confirm the good performance of the proposed technique in terms of accuracy and indicate an increase of convergence rate with respect to the classical approach in many cases. [ABSTRACT FROM AUTHOR]

In this article the multiplicative decomposition of the deformation gradient into one part constrained in the direction of the axis of anisotropy and one part describing the directional deformation is proposed. This leads to a clear division of the deformation and stress states in the direction of anisotropy and a remaining part. The decomposition is explained in detail and a constitutive model of hyper-elasticity is proposed for the case of transversal isotropy, where the behavior of the model is investigated with the aid of simple analytical examples. The model is also investigated for inhomogeneous deformation states using high-order finite elements based on hierarchical shape functions showing the sensitivity of the accuracy of the results in the case of anisotropic media. [ABSTRACT FROM AUTHOR]

SUMMARY Anisotropic elastic materials, such as the homogenized model of a fiber-reinforced matrix, can display near rigidity under certain applied stress-the resulting strains are small compared with the strains that would occur for other stresses of comparable magnitude. The anisotropic material could be rigid under hydrostatic pressure if the material were incompressible, as in isotropic elasticity, but also for other stresses. Some commonly used finite elements are effective in dealing with incompressibility, but are ill-equipped to handle materials that lock under non-hydrostatic stress states (e.g., uniformly reduced serendipity and Q1/Q0 B-bar hexahedra). The failure of the original B-bar method is attributed to the assumption that the mode of deformation to be relieved is one of near incompressibility. The remedy proposed here is based on the spectral decomposition of the compliance matrix of the material. The spectrum can be interpreted to separate nearly-rigid and flexible modes of stress and strain, which leads naturally to a generalized selective reduced integration. Furthermore, the spectral decomposition also enables a three-field elasticity formulation that results in a B-bar method that is effective for general anisotropic materials with an arbitrary nearly-rigid mode of deformation.Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

ABSTRACT Cracked ductile structures yield locally to form a plastic zone ( pz) around their crack tips, which size and shape controls their structural behaviour. Classical pz estimates are based solely on stress intensity factors (SIF), but their precision is limited to very low σn/ SY nominal stress to yield strength ratios. T-stresses are frequently used to correct SIF-based pz estimates, but both SIF and SIF plus T-stress pz estimates are based on truncated linear elastic (LE) stress fields that do not satisfy boundary conditions. Using Griffith's plate complete LE stress field to avoid such truncated pz estimates, the influence of its Williams' series terms on pz estimation is evaluated, showing that T-stress improvements are limited to medium σn/ SY values. Then, corrections are proposed to introduce equilibrium requirements into LE pz estimates. Finally, these improved estimates are compared with pz calculated numerically by an elastic-plastic finite element analysis. [ABSTRACT FROM AUTHOR]

K-dominance of static crack tip in functionally gradient materials (FGMs) with a crack oriented along the direction of the elastic gradient is studied through coherent gradient sensing (CGS), digital speckle correlation method (DSCM) and finite element method (FEM). In the direction of crack propagation, the shear modulus has a linear variation with constant mass density and Poisson's ratio. First, the CGS and DSCM governing equations related to the measurements and the elastic solutions at mode I crack in FGMs are obtained in terms of the stress intensity factor, material constants and graded index. Secondly, two kinds of FGMs specimens and one homogenous specimen are prepared to observe the influences of the property variation on the K-dominance. Then, CGS and DSCM experiments using three-point-bending of FGMs and homogenous beams are performed. Thirdly, based on the results of the experiments, the stress intensity factors of three kinds of specimens are calculated by CGS and DSCM. Meanwhile, the stress intensity factors are obtained by FEM. Finally, comparing the results from CGS, DSCM and FEM, the K-dominance of mode-I static crack tip in FGMs is discussed in detail. [ABSTRACT FROM AUTHOR]

A fatigue crack in steel (CCT geometry) is studied via digital image correlation. The measurement of the stress intensity factor (SIF) change during one cycle is performed using a decomposition of the displacement field onto a tailored set of elastic fields. The same analysis is performed using two different routes, namely, the first one consists in computing the displacement field using a general correlation technique providing the displacement field projected onto finite element shape functions, and then analysing this displacement field in terms of the selected mechanically relevant fields. The second strategy, called integrated approach, directly estimates the amplitude of these elastic fields from the correlation of successive images. Both procedures give consistent results, and offer very good performances in the evaluation of the crack tip position (uncertainty of about 20 μm for a 14.5-mm crack), SIFs (uncertainty <1 MPa ) and opening properties. [ABSTRACT FROM AUTHOR]

Block diagonal preconditioners for the mixed finite element formulation of planar linear elasticity using the PEERS element by Arnold et al. (Jpn. J. Ind. Appl. Math. 1984; 1:347–367) are studied. This mixed finite element approach treats the stress tensor, the displacement field and the anti-symmetric part of the strain tensor as independent variables. The resulting linear system of equations is symmetric but indefinite due to its saddle-point structure. The validity of an inf–sup condition with respect to the H (div,Ω)2 × L2(Ω)2 × L2(Ω) norm suggests an optimal block diagonal preconditioner for the MINRES iterative method. Equivalent preconditioning of the blocks associated with stresses, displacements and anti-symmetric part leads to convergence rates of the block diagonal preconditioner uniformly bounded with respect to the refinement level and the Lamé parameter λ which determines the compressibility of the material. While the L2(Ω) blocks can simply be preconditioned by its diagonal parts, a multilevel technique is employed for the H(div,Ω) block. The smoothing iteration for this technique is based on the discrete Helmholtz decomposition of the underlying finite element space similar to the approach by Hiptmair (Electron. Trans. Numer. Anal. 1997; 6:133–152). Numerical tests for a benchmark problem of planar linear elasticity illustrate the efficiency of this preconditioner, in particular, its level independence and uniform convergence in the incompressible limit. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

ABSTRACT An improvement to the extended finite element method (XFEM) and generalised finite element method (GFEM) is introduced. It enriches the finite element approximation of the crack tip node as well as its surrounding nodes with not only the first term but also the higher order terms of the linear elastic crack tip asymptotic field using a partition of unity method (PUM). Numerical results show that together with a reduced quadrature rule to the enriched elements, this approach predicts accurate stress intensity factors (SIFs) directly (i.e. without extra post-processing) after constraining the enriched nodes properly. However, it does not predict accurately the coefficients of the higher order terms. For that a hybrid crack element (HCE) is introduced which is powerful and convenient not only for directly determining the SIF but also the coefficients of higher order terms in the plane linear elastic crack tip asymptotic field. Finally, the general expressions for the coefficients of the second to fifth terms of the linear elastic crack tip asymptotic field of three-point bend single edge notched beams (TPBs) with span to depth ratios widely used in testing are extended to very deep cracks with the use of the HCE. [ABSTRACT FROM AUTHOR]