... the methods to a linear elasticity model. Findings The authors compute the first- and second-order topological derivatives of the linear elasticity model for various shape functionals in dimension two and three using Amstutz' method, the averaged adjoint method and Delfour's method. Originality/value...

... The elastic energy stored in each of the units under stress or strain decides on stiffer and weaker responses. The pertaining Rayleigh quotient in terms of the flexibility matrices allows bounding the distance of the spring cell models to the finite element in dependence of the triangle configuration...

... to explore in the context of linear elasticity the substitution of the simplex tetrahedral element in space and the triangle in the plane by corresponding spring cells deduced on a flexibility basis using the natural formalism. Design/methodology/approach The natural formalism is characterized...

... and stress along the sides of the triangular element. The associated elastic compliance offers itself for the transition to the spring cell. The diagonal entities are interpreted immediately as springs along the element sides, and the off-diagonal terms account for the completeness of the substitution...

... their advantages and overcome their disadvantages. Design/methodology/approach Herein, a state space BEM in which the SSM is coupled by the BEM is proposed to analyze the elasticity of FGMs, where one BEM domain is set and the others belong to SSM domains. The discretized elements occur only on the boundary...

... Galerkin-SB) algorithm is proposed for the two-dimensional elastic analysis of cyclically symmetric structures. Findings – By utilizing the cyclic symmetry and partitioning algorithm, the whole computational cost can be significantly reduced. Three numerical examples are given to illustrate...

.../methodology/approach – The BFEM uses the base forces given by Gao (2003) as fundamental variables to describe the stress state of an elastic system. An explicit expression of element compliance matrix is derived using the concept of base forces. The detailed formulations of governing equations for the BFEM...

... the number of degree of freedom is twice that of than the truss‐modelled base cell (Sigmund, 1995). Akbar A. Javadi can be contacted at: a.a.javadi@ex.ac.uk © Emerald Group Publishing Limited 2012 Mechanical properties of materials Elasticity Deformation Poisson ratio Auxetic materials...

... the highest stress concentration factor than the standard approaches. © Emerald Group Publishing Limited 2009 Pressure Geometry Stress (materials) Elasticity Finite element analysis a: addendum (mm) b: dedendum (mm) B: gear face width (thickness) (mm) d_r...

... noises and the use of TSVD improves the accuracy. Originality/value It is the first time that the MFS‐DRM is derived to solve three‐dimensional isotropic thermoelastic problems with arbitrary body forces. Elasticity Gaussian processes Although the MFS can reduce the dimensionalities...

...Rita G. Toscano; Eduardo N. Dvorkin Purpose This paper aims to develop a simple and efficient shell element for large strains hyper‐elastic analyses. Design/methodology/approach Based on the classical MITC4 shell element formulation a 3D shell element with finite strain kinematics is developed...

...L. Gallimard Purpose This paper aims to focus on the local quality of outputs of interest computed by a finite element analysis in linear elasticity. Design/methodology/approach In particular outputs of interest are studied which do not depend linearly on the solution of the problem considered...

... with a commercial FEA code was found to be very reliable, time‐effective and can be of great benefit to engineers researching with composites. Research limitations/implications At this state all the materials can only be stressed within their elastic limit. There is no logical impediment to extending...

... 2005 Elasticity Numerical analysis Structures Composite materials have always played an important role in structural engineering. Either through normal manufacturing processes, since material processing cannot always avoid some final flaws such as porosity, or by engineered design...

... materials incorporating classical elastic, viscoelastic, plastic and viscoplastic material description, all operating in the finite strain regime. The underlying rheological model corresponds to the combined action of several rheological components, such as Hooke, Maxwell and Prandtl elements, arranged...

...J.K. Djoko; B.D. Reddy Classical mixed formulations of the boundary‐value problem of linear elasticity are reviewed, and a new three‐field formulation is introduced. The formulation is an extension of the classical Hu‐Washizu approach, and takes the form of a non‐standard mixed problem. Convergence...

...Eugenio Oñate; R.L. Taylor; O.C. Zienkiewicz; J. Rojek In this paper, a residual correction method based upon an extension of the finite calculus concept is presented. The method is described and applied to the solution of a scalar convection‐diffusion problem and the problem of elasticity...

...Kaspar Willam; Inkyu Rhee In this study we examine the spectral properties of stiffness degradation at the constitutive level and at the levels of finite elements and their assemblies. The principal objective is to assess the effects of defects on the elastic stiffness properties at different...

...M.J. García‐Ruíz; G.P. Steven A fixed grid representation of the finite element domain is used to solve elasticity problems. An integration between CAD and FEM systems is made by using this fixed grid representation. Some considerations about FG approximation and stiffness matrix generation...

... investigation with a modal analysis of a single finite element. Details of the calculations involved are summarized in Appendix 2. Section 4 includes a number of representative numerical simulations that assess the performance of these elements in elastic and inelastic problems. Finally, conclusions are drawn...