TY - JOUR A1 - Natarajan, S. A1 - Chakraborty, S. A1 - Thangavel, M. A1 - Bordas, Stéphane Pierre Alain A1 - Rabczuk, Timon T1 - Size dependent free flexural vibration behavior of functionally graded nanoplates JF - Computational Materials Science N2 - Size dependent free flexural vibration behavior of functionally graded nanoplates KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2012 SP - 74 EP - 80 ER - TY - JOUR A1 - Thai, Chien H. A1 - Nguyen-Xuan, Hung A1 - Nguyen-Thanh, Nhon A1 - Le, T.H. A1 - Nguyen-Thoi, T. A1 - Rabczuk, Timon T1 - Static, free vibration and buckling analysis of laminated composite Reissner-Mindlin plates using NURBS-based isogeometric approach JF - International Journal for Numerical Methods in Engineering N2 - This paper presents a novel numerical procedure based on the framework of isogeometric analysis for static, free vibration, and buckling analysis of laminated composite plates using the first-order shear deformation theory. The isogeometric approach utilizes non-uniform rational B-splines to implement for the quadratic, cubic, and quartic elements. Shear locking problem still exists in the stiffness formulation, and hence, it can be significantly alleviated by a stabilization technique. Several numerical examples are presented to show the performance of the method, and the results obtained are compared with other available ones. KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2012 U6 - http://dx.doi.org/10.1002/nme.4282 SP - 571 EP - 603 ER - TY - JOUR A1 - Zhao, Jun-Hua A1 - Guo, Wanlin A1 - Rabczuk, Timon T1 - An analytical molecular mechanics model for the elastic properties of crystalline polyethylene JF - Journal of Applied Physics N2 - We present an analytical model to relate the elastic properties of crystalline polyethylene based on a molecular mechanics approach. Along the polymer chains direction, the united-atom (UA) CH2-CH2 bond stretching, angle bending potentials are replaced with equivalent Euler-Bernoulli beams. Between any two polymer chains, the explicit formulae are derived for the van der Waals interaction represented by the linear springs of different stiffness. Then, the nine independent elastic constants are evaluated systematically using the formulae. The analytical model is finally validated by present united-atom molecular dynamics (MD) simulations and against available all-atom molecular dynamics results in the literature. The established analytical model provides an efficient route for mechanical characterization of crystalline polymers and related materials. KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2012 U6 - http://dx.doi.org/10.1063/1.4745035 ER - TY - JOUR A1 - Jiang, Jin-Wu A1 - Park, Harold S. A1 - Rabczuk, Timon T1 - Enhancing the mass sensitivity of graphene nanoresonators via nonlinear oscillations: The effective strain mechanism JF - Nanotechnology N2 - Enhancing the mass sensitivity of graphene nanoresonators via nonlinear oscillations: The effective strain mechanism KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2012 ER - TY - CHAP A1 - Wudtke, Idna ED - Gürlebeck, Klaus ED - Lahmer, Tom ED - Werner, Frank T1 - CONSTITUTIVE MODELING OF CRYSTALLINE MATERIALS WITH TEXTURE CHARACTERISTICS T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar N2 - The analysis of the response of complex structural systems requires the description of the material constitutive relations by means of an appropriate material model. The level of abstraction of such model may strongly affect the quality of the prognosis of the whole structure. In context to this fact, it is necessary to describe the material in a convenient sense as exact but as simple as possible. All material phenomena of crystalline materials e.g. steel, affecting the behavior of the structure, rely on physical effects which are interacting over spatial scales from subatomic to macroscopic range. Nevertheless, if the material is microscopically heterogenic, it might be appropriate to use phenomenological models for the purpose of civil engineering. Although constantly applied, these models are insufficient for steel materials with microscopic characteristics such as texture, typically occurring in hot rolled steel members or heat affected zones of welded joints. Hence, texture is manifested in crystalline materials as a regular crystallographic structure and crystallite orientation, influencing macroscopic material properties. The analysis of structural response of material with texture (e.g. rolled steel or heat affected zone of a welded joint) obliges the extension of the phenomenological material description of macroscopic scale by means of microscopic information. This paper introduces an enrichment approach for material models based on a hierarchical multiscale methodology. This has been done by describing the grain texture on a mesoscopic scale and coupling it with macroscopic constitutive relations by means of homogenization. Due to a variety of available homogenization methods, the question of an assessment of coupling quality arises. The applicability of the method and the effect of the coupling method on the reliability of the response are presented on an example. KW - Angewandte Informatik KW - Angewandte Mathematik KW - Computerunterstütztes Verfahren Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-27910 UR - http://euklid.bauing.uni-weimar.de/ikm2012 SN - 1611-4086 ER - TY - CHAP A1 - Musial, Michal A1 - Kamiński, Mieczysław A1 - Ubysz, Andrzej ED - Gürlebeck, Klaus ED - Lahmer, Tom ED - Werner, Frank T1 - DISCRETE CRACK MODEL OF BORCZ FOR CALCULATING THE DEFLECTIONS OF BENDING REINFORCED CONCRETE BEAM T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar N2 - In the design of the reinforced concrete beams loaded by the bending moment, it is assumed that the structure can be used at a level of load, that there are local discontinuities - cracks. Designing the element demands checking two limit states of construction, load capacity and usability. Limit states usability include also the deflection of the element. Deflections in the reinforced concrete beams with cracks are based on actual rigidity of the element. After cracking there is a local change in rigidity of the beam. The rigidity is variable in the element’s length and due to the heterogeneous structure of concrete, it is not possible to clearly describe those changes. Most standards of testing methods tend to simplify the calculations and take the average value of the beam’s rigidity on its entire length. The rigidity depends on the level of the maximal load of the beam. Experimental researches verify the value by inserting the coefficients into the formulas used in the theory of elasticity. The researches describe the changes in rigidity in the beam’s length more precisely. The authors take into consideration the change of rigidity, depending on the level of maximum load (continuum models), or localize the changes in rigidity in the area of the cracks (discrete models). This paper presents one of the discrete models. It is distinguished by the fact that the left side of the differential equation, that depends on the rigidity, is constant, and all effects associated with the scratches are taken as the external load and placed on the right side of the equation. This allows to generalize the description. The paper presents a particular integral of the differential equation, which allow analyzing the displacement and vibration for different rigidity of the silo’s walls, the flow rate and type of the flowing material. KW - Angewandte Informatik KW - Angewandte Mathematik KW - Computerunterstütztes Verfahren Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-27907 UR - http://euklid.bauing.uni-weimar.de/ikm2012 SN - 1611-4086 ER - TY - CHAP A1 - Musial, Michal A1 - Ubysz, Andrzej A1 - Ulatowski, Piotr ED - Gürlebeck, Klaus ED - Lahmer, Tom ED - Werner, Frank T1 - MODEL DESCRIBING STATIC AND DYNAMIC DISPLACEMENTS OF SILOS WALL DURING THE FLOW OF LOOSE MATERIAL T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar N2 - Correct evaluation of wall displacements is a key matter when designing silos. This issue is important from both the standpoint of design engineer (load-bearing capacity of structures) and end-consumer (durability of structures). Commonplace methods of silo design mainly focus on satisfying limit states of load-bearing capacity. Current standards fail to specify methods of dynamic displacements analysis. Measurements of stressacting on silo walls prove that the actual stress is sum of static and dynamic stresses. Janssen came up with differential equation describing state of static equilibrium in cross-section of a silo. By solving the equation static stress of granular solid on silo walls can be determined. Equations of motion were determined from equilibrium equations of feature objects. General solution, describing dynamic stresses was presented as parametric model. This paper presents particular integrals of differential equation, which enable analysing displacements and vibrations for different rigidities of silo walls, types of granular solid and its flow rate. KW - Angewandte Informatik KW - Angewandte Mathematik KW - Computerunterstütztes Verfahren Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-27896 UR - http://euklid.bauing.uni-weimar.de/ikm2012 SN - 1611-4086 ER - TY - CHAP A1 - Suzuki, Osamu A1 - Lawrynowicz, Julian A1 - Nouno, Kiyoharu A1 - Nagayama, Daiki ED - Gürlebeck, Klaus ED - Lahmer, Tom ED - Werner, Frank T1 - BINARY AND TERNARY CLIFFORD ANALYSIS ON NONION ALGEBRA AND SU(3) T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar N2 - A concept of non-commutative Galois extension is introduced and binary and ternary extensions are chosen. Non-commutative Galois extensions of Nonion algebra and su(3) are constructed. Then ternary and binary Clifford analysis are introduced for non-commutative Galois extensions and the corresponding Dirac operators are associated. KW - Angewandte Informatik KW - Angewandte Mathematik KW - Computerunterstütztes Verfahren Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-27880 UR - http://euklid.bauing.uni-weimar.de/ikm2012 SN - 1611-4086 ER - TY - CHAP A1 - Stutz, Henning A1 - Wuttke, Frank ED - Gürlebeck, Klaus ED - Lahmer, Tom ED - Werner, Frank T1 - EVALUATION OF SOIL-STRUCTURE INTERACTION MODELS USING DIFFERENT MODEL-ROBUSTNESS APPROACHES T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar N2 - The aim of this study is to show an application of model robustness measures for soilstructure interaction (henceforth written as SSI) models. Model robustness defines a measure for the ability of a model to provide useful model answers for input parameters which typically have a wide range in geotechnical engineering. The calculation of SSI is a major problem in geotechnical engineering. Several different models exist for the estimation of SSI. These can be separated into analytical, semi-analytical and numerical methods. This paper focuses on the numerical models of SSI specific macro-element type models and more advanced finite element method models using contact description as continuum or interface elements. A brief description of the models used is given in the paper. Following this description, the applied SSI problem is introduced. The observed event is a static loaded shallow foundation with an inclined load. The different partial models to consider the SSI effects are assessed using different robustness measures during numerical application. The paper shows the investigation of the capability to use these measures for the assessment of the model quality of SSI partial models. A variance based robustness and a mathematical robustness approaches are applied. These different robustness measures are used in a framework which allows also the investigation of computational time consuming models. Finally the result shows that the concept of using robustness approaches combined with other model–quality indicators (e.g. model sensitivity or model reliability) can lead to unique model–quality assessment for SSI models. KW - Angewandte Informatik KW - Angewandte Mathematik KW - Computerunterstütztes Verfahren Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-27878 UR - http://euklid.bauing.uni-weimar.de/ikm2012 SN - 1611-4086 ER - TY - CHAP A1 - Simsek, Yilmaz ED - Gürlebeck, Klaus ED - Lahmer, Tom ED - Werner, Frank T1 - ON INTERPOLATION FUNCTION OF THE BERNSTEIN POLYNOMIALS T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar N2 - The Bernstein polynomials are used for important applications in many branches of Mathematics and the other sciences, for instance, approximation theory, probability theory, statistic theory, num- ber theory, the solution of the di¤erential equations, numerical analysis, constructing Bezier curves, q-calculus, operator theory and applications in computer graphics. The Bernstein polynomials are used to construct Bezier curves. Bezier was an engineer with the Renault car company and set out in the early 1960’s to develop a curve formulation which would lend itself to shape design. Engineers may …nd it most understandable to think of Bezier curves in terms of the center of mass of a set of point masses. Therefore, in this paper, we study on generating functions and functional equations for these polynomials. By applying these functions, we investigate interpolation function and many properties of these polynomials. KW - Angewandte Informatik KW - Angewandte Mathematik KW - Computerunterstütztes Verfahren Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-27867 UR - http://euklid.bauing.uni-weimar.de/ikm2012 SN - 1611-4086 ER -