### Refine

#### Document Type

- Conference Proceeding (78)
- Article (9)

#### Institute

- In Zusammenarbeit mit der Bauhaus-Universität Weimar (49)
- Institut für Strukturmechanik (19)
- Graduiertenkolleg 1462 (12)
- Juniorprofessur Stochastik und Optimierung (3)
- Professur Angewandte Mathematik (3)
- Institut für Konstruktiven Ingenieurbau (2)
- Institut für Mathematik-Bauphysik (1)
- Professur Stahlbau (1)

#### Keywords

- Angewandte Mathematik (87) (remove)

#### Year of publication

- 2010 (87) (remove)

In the paper presented, reinforced concrete shells of revolution are analyzed in both meridional and circumferential directions. Taking into account the physical non-linearity of the material, the internal forces and the deflections of the shell as well as the strain distribution at the cross-sections are calculated. The behavior of concrete under compression is described by linear and non-linear stress-strain relations. The description of the behavior of concrete under tension must account for tension stiffening effects. A tri-linear function is used to formulate the material law of reinforcement. The problem cannot be solved analytically due to the physical non-linearity. Thus a numerical solution is formulated by means of the LAGRANGE Principle of the minimum of the total potential energy. The kinematically admissible field of deformation is defined by the displacements u in the meridional and w in the radial direction. These displacements must satisfy the equations of compatibility and the kinematical boundary conditions of the shell. The strains are linearly distributed across the wall thickness. The strain energy depends on the specific of the material behavior. Using integral formulations of the material law [1], the strain energy of each part of the cross-section is defined as a function of the strains at the boundaries of the cross-sections. The shell is discretised in the meridional direction. Various methods of numerical differentiation and numerical integration are applied in order to determine the deformations and the strain energy. The unknown displacements u and w are calculated by a non-restricted extremum problem based on the minimum of the total potential energy. From mathematical point of view, the objective function is a convex function, thus the minimum can be determined without difficulty. The advantage of this formulation is that unlike non-linear methods with path-following algorithms the calculation does not have to account for changing stiffness and load increments. All iterations necessary to find the solution are integrated into the “Solver”. The model presented provides many ways of investigating the influence of various material parameters on the stresses and deformations of the entire shell structure.

This paper deals with the modelling and the analysis of masonry vaults. Numerical FEM analyses are performed using LUSAS code. Two vault typologies are analysed (barrel and cross-ribbed vaults) parametrically varying geometrical proportions and constraints. The proposed model and the developed numerical procedure are implemented in a computer analysis. Numerical applications are developed to assess the model effectiveness and the efficiency of the numerical procedure. The main object of the present paper is the development of a computational procedure which allows to define 3D structural behaviour of masonry vaults. For each investigated example, the homogenized limit analysis approach has been employed to predict ultimate load and failure mechanisms. Finally, both a mesh dependence study and a sensitivity analysis are reported. Sensitivity analysis is conducted varying in a wide range mortar tensile strength and mortar friction angle with the aim of investigating the influence of the mechanical properties of joints on collapse load and failure mechanisms. The proposed computer model is validated by a comparison with experimental results available in the literature.

Using a quaternionic reformulation of the electrical impedance equation, we consider a two-dimensional separable-variables conductivity function and, posing two different techniques, we obtain a special class of Vekua equation, whose general solution can be approach by virtue of Taylor series in formal powers, for which is possible to introduce an explicit Bers generating sequence.

In this note, we describe quite explicitly the Howe duality for Hodge systems and connect it with the well-known facts of harmonic analysis and Clifford analysis. In Section 2, we recall briefly the Fisher decomposition and the Howe duality for harmonic analysis. In Section 3, the well-known fact that Clifford analysis is a real refinement of harmonic analysis is illustrated by the Fisher decomposition and the Howe duality for the space of spinor-valued polynomials in the Euclidean space under the so-called L-action. On the other hand, for Clifford algebra valued polynomials, we can consider another action, called in Clifford analysis the H-action. In the last section, we recall the Fisher decomposition for the H-action obtained recently. As in Clifford analysis the prominent role plays the Dirac equation in this case the basic set of equations is formed by the Hodge system. Moreover, analysis of Hodge systems can be viewed even as a refinement of Clifford analysis. In this note, we describe the Howe duality for the H-action. In particular, in Proposition 1, we recognize the Howe dual partner of the orthogonal group O(m) in this case as the Lie superalgebra sl(2 1). Furthermore, Theorem 2 gives the corresponding multiplicity free decomposition with an explicit description of irreducible pieces.

MULTI-SITE CONSTRUCTION PROJECT SCHEDULING CONSIDERING RESOURCE MOVING TIME IN DEVELOPING COUNTRIES
(2010)

Under the booming construction demands in developing countries, particularly in Vietnam situation, construction contractors often perform multiple concurrent projects in different places. In construction project scheduling processes, the existing scheduling methods often assume the resource moving time between activities/projects to be negligible. When multiple projects are deployed in different places and far from each other, this assumption has many shortcomings for properly modelling the real-world constraints. Especially, with respect to developing countries such as the Vietnam which contains transportation systems that are still in backward and low technical standards. This paper proposes a new algorithm named Multi-Site Construction Project Scheduling - MCOPS. The objective of this algorithm is to solve the problem of minimising multi-site construction project duration under limited available conditions of renewable resources (labour, machines and equipment) combining with the moving time of required resource among activities/projects. Additionally, in order to mitigate the impact of resource moving time into the multi-site project duration, this paper proposed a new priority rule: Minimum Resource Moving Time (MinRMT). The MinRMT is applied to rank the finished activities according to a priority order, to support the released resources to the scheduling activities. In order to investigate the impact of the resource moving time among activities during the scheduling process, computational experimentation was implemented. The results of the MCOPS-based computational experiments showed that, the resource moving time among projects has significantly impacted the multi-site project durations and this amount of time can not be ignored in the multi-site project scheduling process. Besides, the efficient application of the MinRMT is also demonstrated through the achieved results of the computational experiment in this paper. Though the efforts in this paper are based on the Vietnamese construction conditions, the proposed method can be usefully applied in other developing countries which have similar construction conditions.

In this paper we consider the time independent Klein-Gordon equation on some conformally flat 3-tori with given boundary data. We set up an explicit formula for the fundamental solution. We show that we can represent any solution to the homogeneous Klein-Gordon equation on the torus as finite sum over generalized 3-fold periodic elliptic functions that are in the kernel of the Klein-Gordon operator. Furthermore we prove Cauchy and Green type integral formulas and set up a Teodorescu and Cauchy transform for the toroidal Klein-Gordon operator. These in turn are used to set up explicit formulas for the solution to the inhomogeneous version of the Klein-Gordon equation on the 3-torus.

A UNIFIED APPROACH FOR THE TREATMENT OF SOME HIGHER DIMENSIONAL DIRAC TYPE EQUATIONS ON SPHERES
(2010)

Using Clifford analysis methods, we provide a unified approach to obtain explicit solutions of some partial differential equations combining the n-dimensional Dirac and Euler operators, including generalizations of the classical time-harmonic Maxwell equations. The obtained regular solutions show strong connections between hypergeometric functions and homogeneous polynomials in the kernel of the Dirac operator.

In this paper we present rudiments of a higher dimensional analogue of the Szegö kernel method to compute 3D mappings from elementary domains onto the unit sphere. This is a formal construction which provides us with a good substitution of the classical conformal Riemann mapping. We give explicit numerical examples and discuss a comparison of the results with those obtained alternatively by the Bergman kernel method.

Tests on Polymer Modified Cement Concrete (PCC) have shown significant large creep deformation. The reasons for that as well as additional material phenomena are explained in the following paper. Existing creep models developed for standard concrete are studied to determine the time-dependent deformations of PCC. These models are: model B3 by Bažant and Bajewa, the models according to Model Code 90 and ACI 209 as well as model GL2000 by Gardner and Lockman. The calculated creep strains are compared to existing experimental data of PCC and the differences are pointed out. Furthermore, an optimization of the model parameters is performed to fit the models to the experimental data to achieve a better model prognosis.

The present article proposes an alternative way to compute the torsional stiffness based on three-dimensional continuum mechanics instead of applying a specific theory of torsion. A thin, representative beam slice is discretized by solid finite elements. Adequate boundary conditions and coupling conditions are integrated into the numerical model to obtain a proper answer on the torsion behaviour, thus on shear center, shear stress and torsional stiffness. This finite element approach only includes general assumptions of beam torsion which are independent of cross-section geometry. These assumptions essentially are: no in-plane deformation, constant torsion and free warping. Thus it is possible to achieve numerical solutions of high accuracy for arbitrary cross-sections. Due to the direct link to three-dimensional continuum mechanics, it is possible to extend the range of torsion analysis to sections which are composed of different materials or even to heterogeneous beams on a high scale of resolution. A brief study follows to validate the implementation and results are compared to analytical solutions.

The article presents analysis of stress distribution in the reinforced concrete support beam bracket which is a component of prefabricated reinforced concrete building. The building structure is spatial frame where dilatations were applied. The proper stiffness of its structure is provided by frames with stiff joints, monolithic lift shifts and staircases. The prefabricated slab floors are supported by beam shelves which are shaped as inverted letter ‘T’. Beams are supported by the column brackets. In order to lower the storey height and fulfill the architectural demands at the same time, the designer lowered the height of beam at the support zone. The analyzed case refers to the bracket zone where the slant crack. on the support beam bracket was observed. It could appear as a result of overcrossing of allowable tension stresses in reinforced concrete, in the bracket zone. It should be noted that the construction solution applied, i.e. concurrent support of the “undercut” beam on the column bracket causes local concentration of stresses in the undercut zone where the strongest transverse forces and tangent stresses occur concurrently. Some additional rectangular stresses being a result of placing the slab floors on the lower part of beam shelves sum up with those described above.

The numerical simulation of microstructure models in 3D requires, due to enormous d.o.f., significant resources of memory as well as parallel computational power. Compared to homogeneous materials, the material hetrogeneity on microscale induced by different material phases demand for adequate computational methods for discretization and solution process of the resulting highly nonlinear problem. To enable an efficient/scalable solution process of the linearized equation systems the heterogeneous FE problem will be described by a FETI-DP (Finite Element Tearing and Interconnecting - Dual Primal) discretization. The fundamental FETI-DP equation can be solved by a number of different approaches. In our approach the FETI-DP problem will be reformulated as Saddle Point system, by eliminating the primal and Lagrangian variables. For the reduced Saddle Point system, only defined by interior and dual variables, special Uzawa algorithms can be adapted for iteratively solving the FETI-DP saddle-point equation system (FETI-DP SPE). A conjugate gradient version of the Uzawa algorithm will be shown as well as some numerical tests regarding to FETI-DP discretization of small examples using the presented solution technique. Furthermore the inversion of the interior-dual Schur complement operator can be approximated using different techniques building an adequate preconditioning matrix and therewith leading to substantial gains in computing time efficiency.

PARAMETER IDENTIFICATION OF MESOSCALE MODELS FROM MACROSCOPIC TESTS USING BAYESIAN NEURAL NETWORKS
(2010)

In this paper, a parameter identification procedure using Bayesian neural networks is proposed. Based on a training set of numerical simulations, where the material parameters are simulated in a predefined range using Latin Hypercube sampling, a Bayesian neural network, which has been extended to describe the noise of multiple outputs using a full covariance matrix, is trained to approximate the inverse relation from the experiment (displacements, forces etc.) to the material parameters. The method offers not only the possibility to determine the parameters itself, but also the accuracy of the estimate and the correlation between these parameters. As a result, a set of experiments can be designed to calibrate a numerical model.

In nonlinear simulations the loading is, in general, applied in an incremental way. Path-following algorithms are used to trace the equilibrium path during the failure process. Standard displacement controlled solution strategies fail if snap-back phenomena occur. In this contribution, a path-following algorithm based on the dissipation of the inelastic energy is presented which allows for the simulation of snap-backs. Since the constraint is defined in terms of the internal energy, the algorithm is not restricted to continuum damage models. Furthermore, no a priori knowledge about the final damage distribution is required. The performance of the proposed algorithm is illustrated using nonlinear mesoscale simulations.

Euclidean Clifford analysis is a higher dimensional function theory offering a refinement of classical harmonic analysis. The theory is centered around the concept of monogenic functions, i.e. null solutions of a first order vector valued rotation invariant differential operator called the Dirac operator, which factorizes the Laplacian. More recently, Hermitean Clifford analysis has emerged as a new and successful branch of Clifford analysis, offering yet a refinement of the Euclidean case; it focusses on the simultaneous null solutions, called Hermitean (or h-) monogenic functions, of two Hermitean Dirac operators which are invariant under the action of the unitary group. In Euclidean Clifford analysis, the Clifford-Cauchy integral formula has proven to be a corner stone of the function theory, as is the case for the traditional Cauchy formula for holomorphic functions in the complex plane. Previously, a Hermitean Clifford-Cauchy integral formula has been established by means of a matrix approach. This formula reduces to the traditional Martinelli-Bochner formula for holomorphic functions of several complex variables when taking functions with values in an appropriate part of complex spinor space. This means that the theory of Hermitean monogenic functions should encompass also other results of several variable complex analysis as special cases. At present we will elaborate further on the obtained results and refine them, considering fundamental solutions, Borel-Pompeiu representations and the Teoderescu inversion, each of them being developed at different levels, including the global level, handling vector variables, vector differential operators and the Clifford geometric product as well as the blade level were variables and differential operators act by means of the dot and wedge products. A rich world of results reveals itself, indeed including well-known formulae from the theory of several complex variables.