Search results

We determine the Hilbert 2-class field tower for some quartic number fields k whose 2-class group Ck,2 is isomorphic to ℤ/2ℤ×ℤ/2ℤ.

The purpose of this paper is to present an efficient return mapping algorithm for elastoplastic constitutive problems of ductile metals with an exact closed form solution of the local constitutive problem in the small strain regime. A Newton Raphson iterative method is adopted for the solution of the boundary value problem.

An efficient return mapping algorithm is illustrated which is based on an elastic predictor and a plastic corrector scheme resulting in an implicit and accurate numerical integration method. Nonlinear kinematic hardening rules and linear isotropic hardening rules are used to describe the components of the hardening variables. In the adopted algorithmic approach the solution of the local constitutive equations reduces to only one straightforward nonlinear scalar equation.

The presented algorithmic scheme naturally leads to a particularly simple form of the nonlinear scalar equation which ultimately scales down to an algebraic (polynomial) equation with a single variable. The straightforwardness of the present approach allows to find the analytical solution of the algebraic equation in a closed form. Further, the consistent tangent operator is derived as associated with the proposed algorithmic scheme and it is shown that the proposed computational procedure ensures a quadratic rate of asymptotic convergence when used with a Newton Raphson iterative method for the global solution procedure.

In the present approach the solution of the algebraic nonlinear equation is found in a closed form and accordingly no iterative method is required to solve the problem of the local constitutive equations. The computational procedure ensures a quadratic rate of asymptotic convergence for the global solution procedure typical of computationally efficient solution schemes. In the paper it is shown that the proposed algorithmic scheme provides an efficient and robust computational solution procedure for elastoplasticity boundary value problems. Numerical examples and computational results are reported which illustrate the effectiveness and robustness of the adopted integration algorithm for the finite element analysis of elastoplastic structures also under elaborate loading conditions.

In this work, the authors aim to employ the so-called linked-interpolation concept already tested on beam and quadrilateral plate finite elements in the design of displacement-based higher-order triangular plate finite elements and test their performance.

Starting from the analogy between the Timoshenko beam theory and the Mindlin plate theory, a family of triangular linked-interpolation plate finite elements of arbitrary order are designed. The elements are tested on the standard set of examples.

The derived elements pass the standard patch tests and also the higher-order patch tests of an order directly related to the order of the element. The lowest-order member of the family of developed elements still suffers from shear locking for very coarse meshes, but the higher-order elements turn out to be successful when compared to the elements from literature for the problems with the same total number of the degrees of freedom.

The elements designed perform well for a number of standard benchmark tests, but the well-known Morley's skewed plate example turns out to be rather demanding, i.e. the proposed design principle cannot compete with the mixed-type approach for this test. Work is under way to improve the proposed displacement-based elements by adding a number of internal bubble functions in the displacement and rotation fields, specifically chosen to satisfy the basic patch test and enable a softer response in the bench-mark test examples.

A new family of displacement-based higher-order triangular Mindlin plate finite elements has been derived. The higher-order elements perform very well, whereas the lowest-order element requires improvement.

This paper aims to investigate the microstructural anisotropy of Ti-6Al-4V samples fabricated by selective laser melting.

Specimens are fabricated through a Renishaw AM400 selective laser melting machine. Three microstructures (as-built, 850°C annealed and 1,050°C annealed) and two building orientations, parallel (PA) and perpendicular (PE) to the building platform, are considered. Starting from in-depth microscopic observations and comprehensive electron backscattered diffraction imaging, the study addresses non-conventional techniques such as internal friction and electrical resistivity measurements to assess the anisotropy of the fabricated parts.

Microscope observations highlight a fine texture with columnar grains parallel to the building direction in the as-built and 850°C annealed samples. Besides, coarse grains characterized the 1,050°C annealed specimens. Internal friction measurements pointed out the presence of internal stress while storage modulus analyses appear sensitive to texture. Electrical resistivity is resulted to be dependent on grain orientation.

The work uses some novel characterization techniques to study the anisotropy and internal stresses of Ti-6Al-4V samples processed by selective laser melting. Mechanical spectroscopy results suitable in this kind of study, as it mimics the operating conditions of the material.

CONSIDER a single rotor helicopter disturbed from the hovering condition as in FIG. 16. It has acquired a small forward velocity V ft./sec. and a nose‐up angular velocity of q rads./sec. For simplicity we consider the centre of gravity of the fuselage to be on the shaft axis, since its actual position can be shown to have a negligible effect in hovering. Resolving moments about the centre of gravity, the important terms are

This study asks whether working in a R&D intensive industry affects a worker's wage profile. If R&D investment translates into transferable human capital or knowledge, workers' mobility constitutes a negative externality from the point of view of the firm/industry that bears the cost of R&D activities. A steepening of the wage profile would address such externality.

Using PSID data combined with US BEA data on US manufacturing industries' R&D intensities between 1981 and 1992, regression analysis is used to explore the hypothesis that, similarly to general training, industry R&D steepens a worker's wage‐experience profile.

In general the evidence is mixed. The results obtained from biennial wage growth regressions support to some extent the hypothesis that exposure to R&D activities allows a specific group of workers to accumulate general human capital for which they pay a positive price in early stages of their career.

An important caveat applies to the results. Unlike previous research by Møen who uses firm level R&D, the results found in this study are generated by using industry level R&D, which, being possibly affected by severe measurement errors, may bias the estimated coefficients towards zero.

This study complements Møen's evidence based on Norwegian wages with the effects of industry‐specific R&D intensities on the earnings profile in US manufacturing industries. By investigating whether industry R&D affects the return to experience and/or to tenure this study addresses an overlooked issue of which type of skills R&D allows workers to accumulate.

This paper aims to present a nonlocal gradient plasticity damage model to demonstrate the crack pattern of a body, in an elastic and plastic state, in terms of damage law. The main objective of this paper is to reconsider the nonlocal theory by including the material in-homogeneity caused by damage and plasticity. The nonlocal nature of the strain field provides a regularization to overcome the analytical and computational problems induced by softening constitutive laws. Such an approach requires C1 continuous approximation. This is achieved by using an isogeometric approximation (IGA). Numerical examples in one and two dimensions are presented.

In this work, the authors propose a nonlocal elastic plastic damage model. The nonlocal nature of the strain field provides a regularization to overcome the analytical and computational problems induced by softening constitutive laws. An additive decomposition of strains in to elastic and inelastic or plastic part is considered. To obtain stable damage, a higher gradient order is considered for an integral equation, which is obtained by the Taylor series expansion of the local inelastic strain around the point under consideration. The higher-order continuity of nonuniform rational B-splines (NURBS) functions used in isogeometric analysis are adopted here to implement in a numerical scheme. To demonstrate the validity of the proposed model, numerical examples in one and two dimensions are presented.

The proposed nonlocal elastic plastic damage model is able to predict the damage in an accurate manner. The numerical results are mesh independent. The nonlocal terms add a regularization to the model especially for strain softening type of materials. The consideration of nonlocality in inelastic strains is more meaningful to the physics of damage. The use of IGA framework and NURBS basis functions add to the nonlocal nature in approximations of the field variables.

The method can be extended to 3D. The model does not consider the effect of temperature and the dissipation of energy due to temperature. The method needs to be implemented for more real practical problems and compare with experimental work. This is an ongoing work.

The nonlocal models are suitable for predicting damage in quasi brittle materials. The use of elastic plastic theories allows to capture the inelastic deformations more accurately.

The nonlocal models are suitable for predicting damage in quasi brittle materials. The use of elastic plastic theories allows to capture the inelastic deformations more accurately.

The present work includes the formulation and implementation of a nonlocal damage plasticity model using an isogeometric discretization, which is the novel contribution of this paper. An implicit gradient enhancement is considered to the inelastic strain. During inelastic deformations, the proposed strain tensor partitioning allows the use of a distinct potential surface and distinct failure criterion for both damage and plasticity models. The use of NURBS basis functions adds to more nonlocality in the approximation.

Double-beam/column systems have drawn much attention in many engineering fields. This work aims to present the free and forced vibrations of a novel and complex double-column system with concentrated masses, axial loads and discrete viscoelastic supports subjected to the excitation of ground acceleration are solved by the extended Laplace transform method (ELTM).

In this work, the authors proposed an extended Laplace transform method (ELTM), which is an exact and explicit analytical method. Firstly, the mathematical model simulating the vibrations of the double-column system is reformulated with Dirac's delta function. Secondly, the exact and explicit mode shape solutions are obtained, based on which the natural frequencies and dynamic responses are obtained. An illustrating example is presented to show the validity of the proposed method. A parametric study is carried out to investigate the influences of the non-dimensional column stiffness ratio and the support stiffness ratio on the peak dynamic displacement and velocity.

It is shown that the proposed method can give exact and explicit solutions of the mode shapes and natural frequencies. It is found that the asynchronous vibrations of the proposed double-column systems can be implemented to efficiently dissipate seismic energy, as shown in the time-histories of displacement and velocity.

This research systematically studied the free and forced vibrations of the complex double-column system. The proposed extended ELTM is a general method. Its application to studying the energy dissipation capability implicates that the double-column system can be utilized to reduce responses in structures under earthquake attacks.

The proposed extended ELTM is original and powerful. Its application to study the complex double-columns system with discrete supports, concentrated masses and axial loads is novel.