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In the current manuscript, the authors examine the Belleville spring with the variable thickness. The thickness is assumed to be variable along the meridional and parallel coordinates of conical coordinate system. The calculation of the Belleville springs includes the cases of the free gliding edges and the edges on cylindric curbs, which constrain the radial movement. The equations developed here are based on common assumptions and are simple enough to be applied to the industrial calculations.

In the current manuscript, the authors examine the Belleville spring with the variable thickness. The calculation of the Belleville springs investigates the free gliding edges and the edges on cylindric curbs with the constrained radial movement. The equations developed here are based on common assumptions and are simple enough to be applied to the industrial calculations.

The developed equations demonstrate that the shift of the inversion point to the inside edge does not influence the bending of the cone. On the contrary, the character of the extensional deformation (circumferential strain) of the middle surface alternates significantly. The extension of the middle surface of free gliding spring occurs outside the inversion. The middle surface of the free gliding spring squeezes inside the inversion point. Contrarily, the complete middle surface of the disk spring on the cylindric curb extends. This behavior influences considerably the function of the spring.

A slotted disk spring consists of two segments: a disk segment and a number of lever arm segments. Currently, the calculation of slotted disk spring is based on the SAE formula (SAE, 1996). This formula is limited to a straight slotted disk spring with freely gliding inner and outer edges.

The equations developed here are based on common assumptions and are simple enough to be applied to the industrial calculations. The developed method is applicable for disk springs with radially constrained edges. The vertical displacements of a disk spring result from an axial load uniformly distributed on inner and outer edges. The method could be directly applied for calculation of slotted disk springs.

The nonlinear governing equations for the of Belleville spring centres were derived. The equations describe the deformation and stresses of thin and moderately thick washers. The variation method is applicable for the disc springs with free gliding and rigidly constrained edges. The developed method is applicable for Belleville spring with radially constrained edges. The vertical displacements of a disc spring result from an axial load uniformly distributed on inner and outer edges.

Presents a finite element formulation of the layout optimization and design sensitivity applied to doubly‐curved shells of revolution. The objectives of the optimization are to maximize buckling pressures and first‐ply‐failure pressures. The problem is formulated and solved with the use of geometrically non‐linear transverse shear shell theory. However, the optimization method proposed limits the sensitivity analysis to a geometrically linear problem. Focuses special attention on the formulation of the optimization problem taking into account various factors, such as the form of geometrical and physical relations, types of design variables and the finite element discretization. Demonstrates several numerical examples to illustrate the capability of the proposed optimization procedures.

The purpose of this paper is to provide an axisymmetric model of tube hydroforming using a Fourier Series based finite element method.

Fourier series interpolation function, which considerably reduces the size of the global stiffness matrix and the number of variables, is employed to approximate displacements. The material of the tube is assumed to be elastic‐plastic and to satisfy the plasticity model that takes into account the rate independent work hardening and normal anisotropy. Numerical solution obtained from an updated Lagrangian formulation of the general shell theory is employed. The axial displacement stroke (a.k.a. axial feed) during tube hydroforming is incorporated using Lagrange multipliers. Contact constraints and boundary friction condition are introduced into the formulation based on the penalty function, which imposes the constraints directly into the tangent stiffness matrix. A forming limit curve based on shear instability and experimental measurements are used as fracture criteria.

The results obtained from this new formulation are compared against the nonlinear finite element code ABAQUS and experimental measurements for isotropic and transversely anisotropic tube materials. The hoop and axial strains predicted with AXHD code compared excellently with those from ABAQUS FEM code using plane stress axisymmetric (SAX1) and four‐node shell (S4R) elements. However, in the case of aluminum, the numerically predicted maximum hoop strain underestimated the actual hoop strain measured from the tube bulging experiment.

The axisymmetric hydroforming program (AXHD) developed in this work is very efficient in simulating the free‐forming stage of the tube hydroforming process under simultaneous action of internal pressurization and displacement stroke.

Although Fourier Series based finite element method has been used in metal forming, the extended application presented in this paper is novel in the finite element analysis of tube hydroforming.

Presents a new B‐spline finite element for the dynamic analysis of unsymmetrical sandwich shells of revolution. The formulation takes account of the membrane and bending effects in isotropic or orthotropic elastic facings, and membrane, bending and transverse shearing effects in an isotropic or othotropic elastic core. Both geometry and local displacements are interpolated by a set of B‐spline functions. The main aspects added by the sandwich structure of the element are the transverse shearing and membrane‐bending coupling effects in the core. These are well represented by a set of new variables which are the mean end relative in‐plane displacements of the facing middle surfaces. Together with the transverse displacement, these variables constitute the degrees of freedom (dofs) of this new B‐spline sandwich element. The finite elements are grouped into super‐elements with C¹ continuity to obtain the whole finite element model. For each super‐element a total of five dofs per node is then obtained except for its end nodes where the derivatives of these dofs with respect to the meridional co‐ordinate are added. This choice reduces to a minimum the total number of dofs in comparison to existing sandwich elements. Evaluates the efficiency and accuracy of the proposed element through several benchmark examples. Compares the results with the analytical and numerical solutions found in the literature. A very satisfactory behaviour of the element was observed in all test cases.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

The purpose of this paper is to present an accurate and efficient element for analysis of spherical shell structures.

A scaled boundary finite element method is proposed, which offers more advantages than the finite element method and boundary element method. Only the boundary of the computational domain needs to be discretized, but no fundamental solution is required.

The method applies to thin as well as thick spherical shells, irrespective of the shell geometry, boundary conditions and applied loading. The numerical solution converges to highly accurate result with raising the order of high-order elements.

The modeling strictly follows three-dimensional theory of elasticity. Formulation of the surface finite elements using three translational degree of freedoms per node is required, which results in considerably simplifying the computation. In the thickness directions, it is solved analytically, no problem of high aspect ratio arises and transverse shear locking can be successfully avoided.

First, a synopsis of the major changes of natural science, mathematics and philosophy within the 17th century shall highlight the birth of the new age of science and technology. Based on Fermat's principle of the shortest light‐way and Galilei's first attempt of an approximative solution of the so‐called Brachistochrone problem using a quarter of the circle, Johann Bernoulli published a competition for this problem in 1696, and six solutions were submitted by the most famous scientists of the time and published in 1697, even though the variational calculus was only published in 1744 by Euler for the first time. Especially the analytical solution of Jakob Bernoulli contains already the main idea of Euler's variational calculus, i.e. to vary only one function value at a time using a finite difference method and proceeding to the infinitesimal limit. Also Leibniz' geometric solution is very remarkable, realizing a direct discrete variational method geometrically which was invented numerically much later in the 19th century by Ritz and Galerkin and generalized to the finite element method by introducing test and trial functions in finite subspaces. A new finite element solution of the non‐linear Brachistochrone problem concludes the paper. It is important to recognize that besides the roots of variational calculus also the first formulations of conservation laws in mechanics and their applications originated in the 17th century.

The purpose of this paper is to describe the development of an electroosmotic dynamic model to simulate the transport phenomena in association with the electric therapy in modern medicine.

The present study builds a new model by employing SUPG finite element method to solve the electroosmotic transport equation in microchannels of human body.

The present electroosmotic finite element analysis demonstrated that the electric treatment has a better curative effect.

The governing electric field equations for tissue fluids in microchannel include the Laplace equation for the effective electrical potential and the Helmholtz equation for the electrical potential established in the electric double layer (EDL). The transport equations governing the hydrodynamic field variables include the mass conservation equation for the electrolyte and the equations of motion for the incompressible charged fluids subject to an electroosmotic body force.

The phenomena of microchannels are dominated by elliptic equations, Laplace, Helmholtz and diffusion equations (Navier Stokes equations at Re=0.0259). These governing equations explain why the reaction of electric treatment is very fast, even immediate.

The analysis of the coupled hydrodynamic and electrical fields, the externally applied electric potential has been shown to be an aid to accelerate the tissue fluid due to the formation of an EDL. Interaction of plasma and tissue fluids in human body is also revealed.

The aim of the present work is to describe a numerical approach to the analysis of three‐dimensional reinforced concrete structures subject to prestressing. The finite element approach developed is described, with particular regard to the configuration of finite elements in relation to numerical model generation. An elasto‐viscoplastic material law is adopted. The non‐linear formulation is discussed, pointing out theoretical and numerical aspects. The computational examples, carried out using a specially developed code, aim at illustrating the characteristic aspects of the proposed approach.

A methodology for producing an elevated-temperature tension stiffening model is presented.

The energy-based stress–strain model of plain concrete developed by Bažant and Oh (1983) was extended to the elevated-temperature domain by developing an analytical formulation for the temperature-dependence of the fracture energy G_f. Then, an elevated-temperature tension stiffening model was developed based on the modification of the proposed elevated-temperature tension softening model.

The proposed tension stiffening model can be used to predict the response of composite floor slabs exposed to fire with great accuracy, provided that the global parameters TS and K_res are adequately calibrated against global structural response data.

In a finite element analysis of reinforced concrete, a tension stiffening model is required as input for concrete to account for actions such as bond slip and tension stiffening. However, an elevated-temperature tension stiffening model does not exist in the research literature. An approach for developing an elevated-temperature tension stiffening model is presented.