Static Reanalysis: A Review

Kassim, A. M. Abu; Topping, B. H. V.

doi:10.1061/(asce)0733-9445(1987)113:5(1029)

Cited by 106 publications

(26 citation statements)

References 64 publications

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“…This technique is probably the fastest reanalysis method, 7 but it is accurate only for small design changes. 10 The linear Taylor series method has been used successfully with the meshless method for optimization (see Refs. 11 and 12).…”

Section: Reanalysis Methodsmentioning

confidence: 99%

Fast Meshless Reanalysis Using Combined Approximations, Preconditioned Conjugate Gradient, and Taylor Series

2006

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Multiple design iterations often require repeated stress analyses to be performed as the design is modified slightly. A method is presented that combines the meshless stress analysis method with a reanalysis technique to avoid repeating the time-consuming steps of remeshing and solving for small design changes. An iterative reanalysis method based on the preconditioned conjugate gradient method is introduced and compared to the linear Taylor series, simple iteration, and combined approximations reanalysis methods. The asymptotic running time is presented for each reanalysis method, and accuracy is compared for two example problems: a cantilever beam and a hole-in-plate. Results show the Taylor series to have the fastest run time, followed in order by simple iteration, preconditioned conjugate gradient, and combined approximations. For the two example problems, accuracy of the simple iteration method is poor for design changes greater than 5%. Taylor series accuracy depends greatly on the choice of the design variable, the example problem, and the method for computing the sensitivity. The combined approximations and preconditioned conjugate gradient methods both demonstrate less than 10% error up to a 100% change in height for the cantilever beam and 30% change in radius for the hole-in-plate example. Multiple design iterations often require repeated stress analyses to be performed as the design is modified slightly. A method is presented that combines the meshless stress analysis method with a reanalysis technique to avoid repeating the time-consuming steps of remeshing and solving for small design changes. An iterative reanalysis method based on the preconditioned conjugate gradient method is introduced and compared to the linear Taylor series, simple iteration, and combined approximations reanalysis methods. The asymptotic running time is presented for each reanalysis method, and accuracy is compared for two example problems: a cantilever beam and a hole-in-plate. Results show the Taylor series to have the fastest run time, followed in order by simple iteration, preconditioned conjugate gradient, and combined approximations. For the two example problems, accuracy of the simple iteration method is poor for design changes greater than 5%. Taylor series accuracy depends greatly on the choice of the design variable, the example problem, and the method for computing the sensitivity. The combined approximations and preconditioned conjugate gradient methods both demonstrate less than 10% error up to a 100% change in height for the cantilever beam and 30% change in radius for the hole-in-plate example. Disciplines Mechanical Engineering Comments Nomenclature

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Section: Reanalysis Methodsmentioning

confidence: 99%

Fast Meshless Reanalysis Using Combined Approximations, Preconditioned Conjugate Gradient, and Taylor Series

2006

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“…While it may be too costly for interactive applications, this can also be efficiently performed using low-rank updating techniques such as for static reanalysis in the engineering community [22]. For surgical simulation, a practical approach has been to use a hybrid domain decomposition approach in which a more easily modified dynamic model is used in a smaller region to be cut [9,17].…”

Section: Elastostatic Modelsmentioning

confidence: 99%

“…In this case, the capacitance matrix completely characterizes the local contact response, since (using (22) in (21))…”

Section: Capacitance Matrix Local Buffer Modelmentioning

confidence: 99%

“…Derived from the Sherman-Morrison-Woodbury formula for lowrank updating of matrix inverses (and factorizations), CMAs have a long history in linear algebra [30,16], where they have been commonly used for static reanalysis [22], to efficiently solve LEM contact mechanics problems [12,25] and more recently for interactive LEM simulations [6,21].…”

Section: Introductionmentioning

confidence: 99%

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A unified treatment of elastostatic contact simulation for real time haptics

James

Pai

2005

ACM SIGGRAPH 2005 Courses on - SIGGRAPH '05

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We describe real-time, physically-based simulation algorithms for haptic interaction with elastic objects. Simulation of contact with elastic objects has been a challenge, due to the complexity of physically accurate simulation and the difficulty of constructing useful approximations suitable for real time interaction. We show that this challenge can be effectively solved for many applications. In particular global deformation of linear elastostatic objects can be efficiently solved with low run-time computational costs, using precomputed Green's functions and fast low-rank updates based on Capacitance Matrix Algorithms. The capacitance matrices constitute exact force response models, allowing contact forces to be computed much faster than global deformation behavior. Vertex pressure masks are introduced to support the convenient abstraction of localized scale-specific point-like contact with an elastic and/or rigid surface approximated by a polyhedral mesh. Finally, we present several examples using the CyberGlove TM and PHANToM TM haptic interfaces.

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“…The engineering community uses updating methods for the analysis of elastic structures undergoing changes, e.g., during a design process, and it is generally referred to as static reanalysis (see [Aro76,KT87,BH93] for comprehensive reviews). These numerous direct solution techniques are very similar to the general matrix updating schemes, and it turns out that many are related to the Sherman-Morrison-Woodbury formula.…”

Section: Static Reanalysis and Contact Mechanicsmentioning

confidence: 99%

Multiresolution green's function methods for interactive simulation of large-scale elastostatic objects

James

Pai

2003

ACM Trans. Graph.

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This thesis presents a framework for low-latency interactive simulation of linear elastostatic models and other systems associated with linear elliptic partial differention equations. This approach makes it feasible to interactively simulate large-scale physical models.Linearity is exploited by formulating the boundary value problem (BVP) solution in terms of Green's functions (GFs) which may be precomputed to provide speed and cheap lookup operations. Runtime BVPs are solved using a collection of Capacitance Matrix Algorithms (CMAs) based on the Sherman-Morrison-Woodbury formula. Temporal coherence is exploited by caching and reusing, as well as sequentially updating, previous capacitance matrix inverses.Multiresolution enhancements make it practical to simulate and store very large models. Efficient compressed representations of precomputed GFs are obtained using secondgeneration wavelets defined on surfaces. Fast inverse wavelet transforms allow fast summation methods to be used to accelerate runtime BVP solution. Wavelet GF compression factors are directly related to interactive simulation speedup, and examples are provided with hundredfold improvements at modest error levels. Furthermore, hierarchical constraints are defined using hierarchical basis functions, and related hierarchical GFs are then used to construct an hierarchical CMA. This direct solution approach is suitable for hard real time simulation since it provides a mechanism for gracefully degrading to coarser resolution approximations, and the wavelet representations allow for runtime adaptive multiresolution rendering.These GF CMAs are well-suited to interactive haptic applications since GFs allow random access to solution components and the capacitance matrix is the contact compliance used for high-fidelity force feedback rendering. Examples are provided for distributed and point-like interactions.Precomputed multizone kinematic GF models are also considered, with examples provided for character animation in computer graphics.Finally, we briefly discuss the generation of multiresolution GF models using either numerical precomputation methods or reality-based robotic measurement.ii

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Static Reanalysis: A Review

Cited by 106 publications

References 64 publications

Fast Meshless Reanalysis Using Combined Approximations, Preconditioned Conjugate Gradient, and Taylor Series

Fast Meshless Reanalysis Using Combined Approximations, Preconditioned Conjugate Gradient, and Taylor Series

A unified treatment of elastostatic contact simulation for real time haptics

Multiresolution green's function methods for interactive simulation of large-scale elastostatic objects

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