Fast Integration of DPG Matrices Based on Sum Factorization for all the Energy Spaces

Numerical integration of the stiffness matrix in higher-order finite element (FE) methods is recognized as one of the heaviest computational tasks in an FE solver. The problem becomes even more relevant when computing the Gram matrix in the algorithm of the Discontinuous Petrov Galerkin (DPG) FE methodology. Making use of 3D tensor-product shape functions, and the concept of sum factorization, known from standard high-order FE and spectral methods, here we take advantage of this idea for the entire exact sequence of FE spaces defined on the hexahedron. The key piece to the presented algorithms is the exact sequence for the one-dimensional element, and use of hierarchical shape functions. Consistent with existing results, the presented algorithms for the integration of {H^{1}}, {H(\operatorname{curl})}, {H(\operatorname{div})}, and {L^{2}} inner products, have the {\mathcal{O}(p^{7})} computational complexity in contrast to the {\mathcal{O}(p^{9})} cost of conventional integration routines. Use of Legendre polynomials for shape functions is critical in this implementation. Three boundary value problems under different variational formulations, requiring combinations of {H^{1}}, {H(\operatorname{div})} and {H(\operatorname{curl})} test shape functions, were chosen to experimentally assess the computation time for constructing DPG element matrices, showing good correspondence with the expected rates.

FASHION AND PATTERN DESIGN OF LADIES’ DRESSES WITH TRANSFORMATION OF DIFFERENT TYPES OF DRAPERIES

One of the ways of creation of new fashion designs is the transformation of a garment in another one. According to the main design principles silhouettes, lines, and forms of elements and pieces can be changed. According to both fashion and technical design the change of the elements with decorative and constructive function is more important than changing only decorative ones. The transformations are possible for all of elements with decorative and constructive function: darts, seams, 3D elements. And according to the fashion and pattern making view the drapery is maybe the most interesting three dimensional element, which can be with only decorative, but in the more of the cases it is with decorative and constructive function. The paper presents fashion and pattern design of ladies’ dresses on the base of transformation of the three basic types of drapes: twist knot, twisted and free draperies. In created variants draperies are with decorative and constructive function. With presented way of transformation new designs of draped ladies’ dresses are easy and successfully created. Every of the basic three types of drapery with decorative and constructive function: twist knot, twisted and free ones can be changed with other two types. The facilitating of design and pattern making is result not only that transformations are made on one basic model, but also that systemized approaches of constructing of twist knot and twisted draperies are used.

A macromodel substitute for simple prediction of the lateral behaviour of composite shear walls

Composite shear wall is a structural component consisting of a steel plate connected using shear tabs to a reinforced concrete cover. The steel plate provides for stiffness, strength, and ductility and the concrete cover prevents the steel plate from buckling. In this paper, effects of steel plate's thickness, compressive strength and thickness of the concrete cover and spacing of the shear tabs on the characteristics of the wall in nonlinear lateral behaviour are evaluated and a macromodel substitute for the wall is developed. The macromodel is a generic lateral force-displacement rule for the wall with its characteristics as developed in this paper. Practical ranges of values are accounted for the parameters involved. Such an approach makes it possible to replace the very complicated and time-consuming three-dimensional model of the composite wall with a simple one-dimensional element following the nonlinear lateral force-displacement path as given in this paper.