Optimal design of high-rise buildings with respect to fundamental eigenfrequency

In modern tall and slender structures, dynamic responses are usually the dominant design requirements, instead of strength criteria. Resonance is often a threatening phenomenon for such structures. To avoid this problem, the fundamental eigenfrequency, an eigenfrequency of higher order, should be maximized. An optimization problem with this objective is constructed in this paper and is applied to a high-rise building. Using variational method, the objective function is maximized, contributing to a particular profile for the first mode shape. Based on this preselected profile, a parametric formulation for flexural stiffness is calculated. Due to some near-zero values for stiffness, the obtained formulation will be modified by adding a lower bound constraint. To handle this constraint some new parameters are introduced; thereby allowing for construction of a model relating the unknown parameters. Based on this mathematical model, a design algorithmic procedure is presented. For the sake of convenience, a single-input design graph is presented as well. The main merit of the proposed method, compared to previous researches, is its hand calculation aspect, suitable for parametric studies and sensitivity analysis. As the presented formulations are dimensionless, they are applicable in any dimensional system. Accuracy and practicality of the proposed method is illustrated at the end by applying it to a real-life structure.

[1]  Kenny C. S Kwok,et al.  Stiffness Optimization for Wind-Induced Dynamic Serviceability Design of Tall Buildings , 2009 .

[2]  M. Bendsøe,et al.  Topology Optimization: "Theory, Methods, And Applications" , 2011 .

[3]  E. Schnack,et al.  A new optimality criteria method for shape optimization of natural frequency problems , 2006 .

[4]  Reza Rahgozar,et al.  A simple analytic method for computing the natural frequencies and mode shapes of tall buildings , 2012 .

[5]  Kenny C. S Kwok,et al.  Integrated wind load analysis and stiffness optimization of tall buildings with 3D modes , 2010 .

[6]  Ahsan Kareem,et al.  Shape and topology sculpting of tall buildings under aerodynamic loads , 2012 .

[7]  Kyoung Sun Moon.  Optimal Configuration of Structural Systems for Tall Buildings , 2012 .

[8]  Giuseppe Brandonisio,et al.  Design criteria for diagrid tall buildings: Stiffness versus strength , 2014 .

[9]  Anil K. Chopra,et al.  Dynamics of Structures: Theory and Applications to Earthquake Engineering , 1995 .

[10]  A. R. Ahmadi,et al.  A simple mathematical model for approximate analysis of tall buildings , 2010 .

[11]  C. C. Pouangare,et al.  Simple Model for Design of Framed‐Tube Structures , 1991 .

[12]  Jerome J. Connor,et al.  Structural Motion Engineering , 2014 .

[13]  Nima Yaghoobi,et al.  TOPOLOGICAL OPTIMIZATION OF VIBRATING CONTINUUM STRUCTURES FOR OPTIMAL NATURAL EIGENFREQUENCY , 2017 .

[14]  Kyoung Sun Moon,et al.  Stiffness-based design methodology for steel braced tube structures: A sustainable approach , 2010 .

[15]  Bryan,et al.  Tall building structures , 1991 .

[16]  Reza Rahgozar,et al.  Approximate analysis of tall buildings using sandwich beam models with variable cross‐section , 2008 .

[17]  I. D. Bennetts,et al.  Structural Systems for Tall Buildings , 1995 .

[18]  Jerome J. Connor,et al.  Diagrid structural systems for tall buildings: characteristics and methodology for preliminary design , 2007 .

[19]  Glaucio H. Paulino,et al.  Application of layout and topology optimization using pattern gradation for the conceptual design of buildings , 2011 .

[20]  Hojjat Adeli,et al.  Advances in optimization of highrise building structures , 2014 .

[21]  Akh Kwan.  Simple Method for Approximate Analysis of Framed Tube Structures , 1994 .

[22]  Kaiqiang Ma,et al.  Calculation model of the lateral stiffness of high‐rise diagrid tube structures based on the modular method , 2017 .

[23]  Guangyao Li,et al.  Topology optimization of free vibrating continuum structures based on the element free Galerkin method , 2012 .