The virtual distortion method—a versatile reanalysis tool for structures and systems

For 20 years of development, the virtual distortion method (VDM) has proved to be a versatile reanalysis tool in various applications, including structures and truss-like systems. This article presents a summary of principal achievements, demonstrating the capabilities of the VDM both in statics and dynamics, in linear and nonlinear analysis. The major advantage of VDM is its exactness and no need for matrix inversion in the reanalysis algorithm. The influence matrix—numerical core of the VDM—contains the whole mechanical knowledge about a structure, by looking at all global responses due to local disturbances. The strength of the method is demonstrated for truss structures.

[1]  Jan Holnicki-Szulc,et al.  Damage Identification by the Dynamic Virtual Distortion Method , 2004 .

[2]  Su-huan Chen,et al.  Comparison of several eigenvalue reanalysis methods for modified structures , 2000 .

[3]  M. Ghosn,et al.  PSEUDOFORCE METHOD FOR NONLINEAR ANALYSIS AND REANALYSIS OF STRUCTURAL SYSTEMS , 2001 .

[4]  Giuseppe Muscolino,et al.  Dynamically Modified Linear Structures: Deterministic and Stochastic Response , 1996 .

[5]  Jan Holnicki-Szulc,et al.  Structural modifications simulated by virtual distortions , 1989 .

[6]  Structural reanalysis in configuration space by perturbation approach: A real mode method , 1996 .

[7]  G. Maier A matrix structural theory of piecewise linear elastoplasticity with interacting yield planes , 1970 .

[8]  Jan Holnicki-Szulc,,et al.  Review of Virtual Distortion Method and Its Applications to Fast Redesign and Sensitivity Analysis , 2000 .

[9]  Uri Kirsch,et al.  A unified reanalysis approach for structural analysis, design, and optimization , 2003 .

[10]  Jan Holnicki-Szulc,et al.  Health Monitoring of Electric Circuits , 2005 .

[11]  J. Argyris,et al.  Elasto-plastic Matrix Displacement Analysis of Three-dimensional Continua , 1965, The Journal of the Royal Aeronautical Society.

[12]  Don Cronin,et al.  Eigenvalue and eigenvector determination for nonclassically damped dynamic systems , 1990 .

[13]  Jan Holnicki-Szulc,et al.  Leakage Detection in Water Networks , 2005 .

[14]  U. Kirsch,et al.  Exact structural reanalysis by a first-order reduced basis approach , 1995 .

[15]  Uri Kirsch,et al.  Nonlinear dynamic reanalysis of structures by combined approximations , 2006 .

[16]  Antonina Pirrotta,et al.  Stochastic dynamics of linear elastic trusses in presence of structural uncertainties (virtual distortion approach) , 2004 .

[17]  Barry Hilary Valentine Topping,et al.  Static Reanalysis: A Review , 1987 .

[18]  Jan Holnicki-Szulc,et al.  Adaptive crashworthiness concept , 2004 .

[19]  Josep Vehí,et al.  Two Approaches to Structural Damage Identification: Model Updating versus Soft Computing , 2006 .

[20]  Niels C. Lind Analysis of Structures by System Theory , 1962 .

[21]  E. Kröner,et al.  Kontinuumstheorie der Versetzungen und Eigenspannungen , 1958 .

[22]  H. Miura,et al.  An approximate analysis technique for design calculations , 1971 .

[23]  Barry Hilary Valentine Topping,et al.  The use and efficiency of the theorems of structural variation for finite element analysis , 1987 .

[24]  Jan Holnicki-Szulc,et al.  Virtual Distortion Method , 1991 .

[25]  Ahmed K. Noor,et al.  Approximate techniques of strctural reanalysis , 1974 .

[26]  Hardy Cross,et al.  Analysis of flow in networks of conduits or conductors , 1936 .

[27]  Hua-Peng Chen,et al.  Efficient methods for determining modal parameters of dynamic structures with large modifications , 2006 .

[28]  Jan Holnicki-Szulc,et al.  Design of Adaptive Structures for Improved Load Capacity , 1998 .

[29]  Zhong-Sheng Liu,et al.  Structural modal reanalysis for topological modifications of finite element systems , 2000 .

[30]  Jan Holnicki-Szulc,et al.  Structural analysis, design and control by the virtual distortion method , 1995 .

[31]  Jan Holnicki-Szulc,et al.  High-performance impact absorbing materials—the concept, design tools and applications , 2003 .

[32]  Przemysław Kołakowski,et al.  SENSITIVITY ANALYSIS OF TRUSS STRUCTURES (VIRTUAL DISTORTION METHOD APPROACH) , 1998 .

[33]  J. Hurtado Reanalysis of linear and nonlinear structures using iterated Shanks transformation , 2002 .

[34]  Ross B. Corotis,et al.  Nonlinear Analysis of Frame Structures by Pseudodistortions , 1999 .

[36]  Liang-Jenq Leu,et al.  Applications of a reduction method for reanalysis to nonlinear dynamic analysis of framed structures , 2000 .

[37]  Keng C. Yap,et al.  A COMPARATIVE STUDY OF STRUCTURAL DYNAMIC MODIFICATION AND SENSITIVITY METHOD APPROXIMATION , 2002 .

[38]  Pierfrancesco Cacciola,et al.  A dynamic reanalysis technique for general structural modifications under deterministic or stochastic input , 2005 .

[39]  J. -F. M. Barthelemy,et al.  Approximation concepts for optimum structural design — a review , 1993 .

[40]  Mehmet Polat Saka The theorems of structural variation for solid cubic finite elements , 1998 .

[41]  Ramana V. Grandhi,et al.  Successive Matrix Inversion Method for Reanalysis of Engineering Structural Systems , 2004 .

[42]  M. Di Paola,et al.  Probabilistic analysis of truss structures with uncertain parameters (virtual distortion method approach) , 2004 .

[43]  Ross B. Corotis,et al.  Reanalysis of rigid frame structures by the virtual distortion method , 1996 .

[44]  Raphael T. Haftka,et al.  Fast exact linear and non‐linear structural reanalysis and the Sherman–Morrison–Woodbury formulas , 2001 .

[45]  Michael D. Grissom,et al.  A reduced eigenvalue method for broadband analysis of a structure with vibration absorbers possessing rotatory inertia , 2005 .

[46]  K. I. Majid,et al.  The elastic–plastic analysis of frames by the theorems of structural variation , 1985 .