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- In Zusammenarbeit mit der Bauhaus-Universität Weimar (15) (remove)

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- 2015 (15) (remove)

The p-Laplace equation is a nonlinear generalization of the Laplace equation. This generalization is often used as a model problem for special types of nonlinearities. The p-Laplace equation can be seen as a bridge between very general nonlinear equations and the linear Laplace equation. The aim of this paper is to solve the p-Laplace equation for 2 < p < 3 and to find strong solutions. The idea is to apply a hypercomplex integral operator and spatial function theoretic methods to transform the p-Laplace equation into the p-Dirac equation. This equation will be solved iteratively by using a fixed point theorem.

Recently there has been a surge of interest in PDEs involving fractional derivatives in different fields of engineering. In this extended abstract we present some of the results developedin [3]. We compute the fundamental solution for the three-parameter fractional Laplace operator Δ by transforming the eigenfunction equation into an integral equation and applying the method of separation of variables. The obtained solutions are expressed in terms of Mittag-Leffer functions. For more details we refer the interested reader to [3] where it is also presented an operational approach based on the two Laplace transform.

The theory of regular quaternionic functions of a reduced quaternionic variable is a 3-dimensional generalization of complex analysis. The Moisil-Theodorescu system (MTS) is a regularity condition for such functions depending on the radius vector r = ix+jy+kz seen as a reduced quaternionic variable. The analogues of the main theorems of complex analysis for the MTS in quaternion forms are established: Cauchy, Cauchy integral formula, Taylor and Laurent series, approximation theorems and Cauchy type integral properties. The analogues of positive powers (inner spherical monogenics) are investigated: the set of recurrence formulas between the inner spherical monogenics and the explicit formulas are established. Some applications of the regular function in the elasticity theory and hydrodynamics are given.

It is well-known that the solution of the fundamental equations of linear elasticity for a homogeneous isotropic material in plane stress and strain state cases can be equivalently reduced to the solution of a biharmonic equation. The discrete version of the Theorem of Goursat is used to describe the solution of the discrete biharmonic equation by the help of two discrete holomorphic functions. In order to obtain a Taylor expansion of discrete holomorphic functions we introduce a basis of discrete polynomials which fulfill the so-called Appell property with respect to the discrete adjoint Cauchy-Riemann operator. All these steps are very important in the field of fracture mechanics, where stress and displacement fields in the neighborhood of singularities caused by cracks and notches have to be calculated with high accuracy. Using the sum representation of holomorphic functions it seems possible to reproduce the order of singularity and to determine important mechanical characteristics.

Performing parameter identification prior to numerical simulation is an essential task in geotechnical engineering. However, it has to be kept in mind that the accuracy of the obtained parameter is closely related to the chosen experimental setup, such as the number of sensors as well as their location. A well considered position of sensors can increase the quality of the measurement and to reduce the number of monitoring points. This Paper illustrates this concept by means of a loading device that is used to identify the stiffness and permeability of soft clays. With an initial setup of the measurement devices the pore water pressure and the vertical displacements are recorded and used to identify the afore mentioned parameters. Starting from these identified parameters, the optimal measurement setup is investigated with a method based on global sensitivity analysis. This method shows an optimal sensor location assuming three sensors for each measured quantity, and the results are discussed.

SELECTION AND SCALING OF GROUND MOTION RECORDS FOR SEISMIC ANALYSIS USING AN OPTIMIZATION ALGORITHM
(2015)

The nonlinear time history analysis and seismic performance based methods require a set of scaled ground motions. The conventional procedure of ground motion selection is based on matching the motion properties, e.g. magnitude, amplitude, fault distance, and fault mechanism. The seismic target spectrum is only used in the scaling process following the random selection process. Therefore, the aim of the paper is to present a procedure to select a sets of ground motions from a built database of ground motions. The selection procedure is based on running an optimization problem using Dijkstra’s algorithm to match the selected set of ground motions to a target response spectrum. The selection and scaling procedure of optimized sets of ground motions is presented by examining the analyses of nonlinear single degree of freedom systems.

VARIATIONAL POSITING AND SOLUTION OF COUPLED THERMOMECHANICAL PROBLEMS IN A REFERENCE CONFIGURATION
(2015)

Variational formulation of a coupled thermomechanical problem of anisotropic solids for the case of non-isothermal finite deformations in a reference configuration is shown. The formulation of the problem includes: a condition of equilibrium flow of a deformation process in the reference configuration; an equation of a coupled heat conductivity in a variational form, in which an influence of deformation characteristics of a process on the temperature field is taken into account; tensor-linear constitutive relations for a hypoelastic material; kinematic and evolutional relations; initial and boundary conditions. Based on this formulation several axisymmetric isothermal and coupled problems of finite deformations of isotropic and anisotropic bodies are solved. The solution of coupled thermomechanical problems for a hollow cylinder in case of finite deformation showed an essential influence of coupling on distribution of temperature, stresses and strains. The obtained solutions show the development of stressstrain state and temperature changing in axisymmetric bodies in the case of finite deformations.

In this paper we present some rudiments of a generalized Wiman-Valiron theory in the context of polymonogenic functions. In particular, we analyze the relations between different notions of growth orders and the Taylor coefficients. Our main intention is to look for generalizations of the Lindel¨of-Pringsheim theorem. In contrast to the classical holomorphic and the monogenic setting we only obtain inequality relations in the polymonogenic setting. This is due to the fact that the Almansi-Fischer decomposition of a polymonogenic function consists of different monogenic component functions where each of them can have a totally different kind of asymptotic growth behavior.

Steel profiles with slender cross-sections are characterized by their high susceptibility to instability phenomena, especially local buckling, which are intensified under fire conditions. This work presents a study on numerical modelling of the behaviour of steel structural elements in case of fire with slender cross-sections. To accurately carry out these analyses it is necessary to take into account those local instability modes, which normally is only possible with shell finite elements. However, aiming at the development of more expeditious methods, particularly important for analysing complete structures in case of fire, recent studies have proposed the use of beam finite elements considering the presence of local buckling through the implementation of a new effective steel constitutive law. The objective of this work is to develop a study to validate this methodology using the program SAFIR. Comparisons are made between the results obtained applying the referred new methodology and finite element analyses using shell elements. The studies were made to laterally restrained beams, unrestrained beams, axially compressed columns and columns subjected to bending plus compression.

Portugal is one of the European countries with higher spatial and population freeway network coverage. The sharp growth of this network in the last years instigates the use of methods of analysis and the evaluation of their quality of service in terms of the traffic performance, typically performed through internationally accepted methodologies, namely that presented in the Highway Capacity Manual (HCM). Lately, the use of microscopic traffic simulation models has been increasingly widespread. These models simulate the individual movement of the vehicles, allowing to perform traffic analysis. The main target of this study was to verify the possibility of using microsimulation as an auxiliary tool in the adaptation of the methodology by HCM 2000 to Portugal. For this purpose, were used the microscopic simulators AIMSUN and VISSIM for the simulation of the traffic circulation in the A5 Portuguese freeway. The results allowed the analysis of the influence of the main geometric and traffic factors involved in the methodology by HCM 2000. In conclusion, the study presents the main advantages and limitations of the microsimulators AIMSUN and VISSIM in modelling the traffic circulation in Portuguese freeways. The main limitation is that these microsimulators are not able to simulate explicitly some of the factors considered in the HCM 2000 methodology, which invalidates their direct use as a tool in the quantification of those effects and, consequently, makes the direct adaptation of this methodology to Portugal impracticable.