This study focuses on the shape optimization of concrete gravity dams considering dam–water–foundation interaction and nonlinear effects subject to earthquake. The concrete gravity dam is considered as a two–dimensional structure involving the geometry and material nonlinearity effects. For the description of the nonlinear behavior of concrete material under earthquake loads, the Drucker–Prager...

The aim of this paper is to numerically investigate the development, thickness and orientation of shear bands, in biaxial test with two approaches towards solving problems of continuum mechanics, namely the meshless "Soft PARticle" method and the mesh based Finite Element method. Soft PArticle Code (SPARC) is a straightforward collocation numerical method based on strong formulation, in which a...

We study the computation of the orthogonal spline collocation solution of a linear Dirichlet boundary value problem with a nonselfadjoint or an indefinite operator of the form Lu = ∑ aij(x)uxixj + ∑ bi(x)uxi + c(x)u. We apply a preconditioned conjugate gradient method to the normal system of collocation equations with a preconditioner associated with a separable operator, and prove that the res...

We consider the computationally intense problem of solving the large, sparse and non-symmetric system of equations arising from the discretization of elliptic Boundary Value Problems (BVPs) by the Collocation finite element method using Hermite bi-cubic elements. As the size of the problem directly suggests the usage of parallel iterative methods, we consider the implementation on multiprocesso...

This chapter provides a brief literature review together with detailed descriptions of the authors’ work on the stability and control of systems represented by linear time-periodic delay-differential equations using the Chebyshev and temporal finite element analysis (TFEA) techniques. Here, the theory and examples assume that there is a single fixed discrete delay which is equal to the principa...

We extend the development of collocation methods within the framework of Isogeometric Analysis (IGA) to multi-patch NURBS configurations, various boundary and patch interface conditions, and explicit dynamic analysis. The methods developed are higher-order accurate, stable with no hourglass modes, and efficient in that they require a minimum number of quadrature evaluations. The combination of ...