构造上正交各向异性凹凸板等效刚度的研究
|
摘要
针对构造上正交各向异性凹凸板等效刚度的研究问题,考虑经典弹性薄板理论和凹凸板的几何周期特性,划分出了以凸起为中心的典型单元,首先研究了典型单元的刚度特性,再通过刚度组合方法得到了凹凸板的等效弯曲刚度;然后以四边简支正交各向异性凹凸板为例,基于经典薄板理论中纳维二重三角级数推广到正交各向异性板的解,利用本文的等效刚度公式分别计算了在集中载荷作用下板的挠度和其自身的固有频率。计算结果与ANSYS有限元的模拟结果进行对比,理论计算与有限元模拟结果一致,验证了本文等效解析方法的合理性和精确性。最后讨论了凹凸板的各项尺寸参数对刚度等效精度的影响,并对其原因进行了分析。本文给出的等效刚度解析方法便于工程应用,尤其在应对大规模凹凸板刚度求解中具有计算简便的优点,研究结果对凹凸板静力学和动力学的研究以及实际工程应用具有重要的指导意义。
According to the construction orthogonal anisotropy truss core panel and based on the theory of elastic thin plate and truss core panel geometry periodically, the plate is divided into typical element with the saddle-backing as a center. The stiffness characteristic of typical element is investigated, and the equivalent bending stiffness of truss core panel is obtained by the method of stiffness combination. Take the orthogonal anisotropy truss core panel with four sides simply supported under the concentrated load as an example, based on the classical thin plate theory of Navier-Dual trigonometric series promotion to solutions of orthogonal anisotropy plate, the deflection of plate is calculated by the equivalent stiffness formula and compared with the simulation results by FEM(Finite Element Modeling) of ANSYS. The rationality and accuracy of equivalent stiffness is verified. Influence of the size parameters of truss core panel on the stiffness equivalent accuracy is researched and the reason is analyzed. The natural frequency of rectangular truss core panel with four sides simply supported is calculated by the equivalent stiffness. The FEM results are in agreement with the theoretical calculation results which verify the correctness of the equivalent stiffness. Results obtained in the present study have important meanings for the statics and dynamics analysis of the truss core panels and practical engineering applications..
According to the construction orthogonal anisotropy truss core panel and based on the theory of elastic thin plate and truss core panel geometry periodically, the plate is divided into typical element with the saddle-backing as a center. The stiffness characteristic of typical element is investigated, and the equivalent bending stiffness of truss core panel is obtained by the method of stiffness combination. Take the orthogonal anisotropy truss core panel with four sides simply supported under the concentrated load as an example, based on the classical thin plate theory of Navier-Dual trigonometric series promotion to solutions of orthogonal anisotropy plate, the deflection of plate is calculated by the equivalent stiffness formula and compared with the simulation results by FEM(Finite Element Modeling) of ANSYS. The rationality and accuracy of equivalent stiffness is verified. Influence of the size parameters of truss core panel on the stiffness equivalent accuracy is researched and the reason is analyzed. The natural frequency of rectangular truss core panel with four sides simply supported is calculated by the equivalent stiffness. The FEM results are in agreement with the theoretical calculation results which verify the correctness of the equivalent stiffness. Results obtained in the present study have important meanings for the statics and dynamics analysis of the truss core panels and practical engineering applications..
引文
[1]LIAO Y,ZHAO X,ISHIDA S,et al.3D origami structure design and simulation by parametric origami module[M].Berlin,Gemany:Springer-Verlag,2012:228-240.
[2]XIA Z Z,ZHAO X L,HAGIWARA I.A simulation approach to improve forming limitation of truss core panel[J].Applied mechanics&materials,2012,121-126:2471-2475.
[3]TOKURA S,HAGIWARA I.Forming process simulation of truss core panel[J].Journal of computational science&technology,2010,4(4):25-35.
[4]YANG Y,XIA Z,ZHAO X,et al.Comprehensive optimization for raised floor structure using origami engineering[J].Communications in computer and information science,2012,326:216-227.
[5]NOJIMA T.Foldable tubes and conical shells consisting of differently shaped elements.origami-modelling of non-circular tubes and conical shells[J].Transactions of the Japan society of mechanical engineers,2002,68(667):1015-1020.
[6]WILLIAMS M L.Surface stress singularities resulting from various boundary conditions in angular corners of plates under bending[J].JOM,1952,19(12):1-7.
[7]SEYDEL E.Wrinkling of reinforced plates subjected to shear stresses[J].Technical report archive&image library,1931,57(1):1-71.
[8]JOHNS J.Shear buckling of isotropic and orthotropic plates:a review[R].Britian:British Aircraft Corporation,1971:1-34.
[9]黄川腾,王志军,邓然,等.考虑剪切变形的箱型空心楼盖拟板法研究[J].工程力学,2015(12):198-207.(HUANG Chuanteng,WANG Zhijun,DENG Ran,et al.Study on analogue slab method considering shear deformation for box-filler hollow floor[J].Engineering mechanics,2015,32(12):198-207(in Chinese)).
[10]TAKABATAKE H.Dynamic analyses of elastic plates with voids[J].International journal of solids and structures,1991,28(7):879-895.
[11]TAKABATAKE H.Static analyses of elastic plates with voids[J].International journal of solids and structures,1991,28(2):179-196.
[12]胡肇滋,钱寅泉.正交构造异性板刚度计算的探讨[J].土木工程学报,1987,20(4):49-61.(HU Zhaozi,QIAN Yinquan.Research on the calculation of structurally orthotropic plate rigidity[J].China civil engineering journal,1987,20(4):49-61(in Chinese)).
[13]程远兵,程文瀼,党纪.均布荷载下四边简支蜂窝式空心板的解析解[J].工程力学,2009,26(8):34-38.(CHENG Yuanbing,CHENG Wenrang,DANG Ji.Analytical solution of cellular hollow plates simply supported subjected to uniformly distributed loads[J].Engineering mechanics,2009,26(8):34-38(in Chinese)).
[14]MARCUZZI A,MORASSI A.Dynamic identification of a concrete bridge with orthotropic plate-type deck[J].Journal of structural engineering,2010,136(5):586-602.
[15]张福范.弹性薄板[M].北京:科学出版社,1984:30-33,58-61,159-161.(ZHANG Fufan.Elastic thin plate[M].Beijing:Science Press,1984:30-33,58-61,159-161(in Chinese)).
[2]XIA Z Z,ZHAO X L,HAGIWARA I.A simulation approach to improve forming limitation of truss core panel[J].Applied mechanics&materials,2012,121-126:2471-2475.
[3]TOKURA S,HAGIWARA I.Forming process simulation of truss core panel[J].Journal of computational science&technology,2010,4(4):25-35.
[4]YANG Y,XIA Z,ZHAO X,et al.Comprehensive optimization for raised floor structure using origami engineering[J].Communications in computer and information science,2012,326:216-227.
[5]NOJIMA T.Foldable tubes and conical shells consisting of differently shaped elements.origami-modelling of non-circular tubes and conical shells[J].Transactions of the Japan society of mechanical engineers,2002,68(667):1015-1020.
[6]WILLIAMS M L.Surface stress singularities resulting from various boundary conditions in angular corners of plates under bending[J].JOM,1952,19(12):1-7.
[7]SEYDEL E.Wrinkling of reinforced plates subjected to shear stresses[J].Technical report archive&image library,1931,57(1):1-71.
[8]JOHNS J.Shear buckling of isotropic and orthotropic plates:a review[R].Britian:British Aircraft Corporation,1971:1-34.
[9]黄川腾,王志军,邓然,等.考虑剪切变形的箱型空心楼盖拟板法研究[J].工程力学,2015(12):198-207.(HUANG Chuanteng,WANG Zhijun,DENG Ran,et al.Study on analogue slab method considering shear deformation for box-filler hollow floor[J].Engineering mechanics,2015,32(12):198-207(in Chinese)).
[10]TAKABATAKE H.Dynamic analyses of elastic plates with voids[J].International journal of solids and structures,1991,28(7):879-895.
[11]TAKABATAKE H.Static analyses of elastic plates with voids[J].International journal of solids and structures,1991,28(2):179-196.
[12]胡肇滋,钱寅泉.正交构造异性板刚度计算的探讨[J].土木工程学报,1987,20(4):49-61.(HU Zhaozi,QIAN Yinquan.Research on the calculation of structurally orthotropic plate rigidity[J].China civil engineering journal,1987,20(4):49-61(in Chinese)).
[13]程远兵,程文瀼,党纪.均布荷载下四边简支蜂窝式空心板的解析解[J].工程力学,2009,26(8):34-38.(CHENG Yuanbing,CHENG Wenrang,DANG Ji.Analytical solution of cellular hollow plates simply supported subjected to uniformly distributed loads[J].Engineering mechanics,2009,26(8):34-38(in Chinese)).
[14]MARCUZZI A,MORASSI A.Dynamic identification of a concrete bridge with orthotropic plate-type deck[J].Journal of structural engineering,2010,136(5):586-602.
[15]张福范.弹性薄板[M].北京:科学出版社,1984:30-33,58-61,159-161.(ZHANG Fufan.Elastic thin plate[M].Beijing:Science Press,1984:30-33,58-61,159-161(in Chinese)).