Adaptive dynamic relaxation algorithm for non-linear hyperelastic structures Part I. Formulation

Oakley, David R.; Knight, Norman F.

doi:10.1016/0045-7825(95)00805-b

Cited by 76 publications

(42 citation statements)

References 33 publications

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“…Dynamic relaxation method [15][16] has been popularly used in many numerical analysis fields such as linear elastic analysis of thin shells and vaults, load analysis of spatial or planar frames and form finding or load analysis of tensile structures. The pseudo mass or pseudo damping is used to change a static problem into a dynamic one, so it is also called as pseudo transient analysis method.…”

Section: Dynamic Relaxation Methodsmentioning

confidence: 99%

Structural Design of a Practical Large-Span Cable-Frame Type of Suspended Single-Layer Reticulated Shell With Free Surface

Shi-lin¹

2011

Volume 7 Number 4

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Cable-frame type of suspended single-layer reticulated shells with free surface proposed by the author of the present paper is a novel type of large-span hybrid spatial structures. The whole design procedure regarding a practical gymnasium steel roof using this structural system is presented. System constitution including form finding of the upper structure and shape determination analysis of the lower cable-bar system is given out in details and emphasized. Load/action effects are thoroughly summarized for member sections design. A special joint design when diagonal cables penetrating the corresponding upper steel beam member is also brought forward. Hopefully the present paper could benefit the further research and practical engineering on hybrid spatial structures.

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Section: Dynamic Relaxation Methodsmentioning

confidence: 99%

Structural Design of a Practical Large-Span Cable-Frame Type of Suspended Single-Layer Reticulated Shell With Free Surface

Shi-lin¹

2011

Volume 7 Number 4

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“…First, the explicit formulation makes it easy to program. Secondly, the vectorized formulation makes the parallelization straightforward [74,75,76], reduces the memory consumption, and increases the efficiency of computation as vectorized operations can be optimized by contemporary compilers and CPUs. Thirdly, it is convenient to treat the local kinematic constraints like contacts or bound constraints, which can be directly applied in the Predictor step.…”

Section: Apply Boundary Conditions and Initialize U(k) Set V(k)mentioning

confidence: 99%

Computational modeling of size-dependent superelasticity of shape memory alloys

Qiao

Radovitzky

2016

Journal of the Mechanics and Physics of Solids

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The superelastic effect in shape memory alloys (SMAs) is attributed to the stressinduced reversible austenitic-martensitic phase transformations. It is characterized by the development of significant strains which are fully recoverable upon unloading, and also characterized by the stress-hysteresis in the loading and unloading cycle which corresponds to the energy dissipated during phase transformations. Recently, experiments have revealed size-dependent effects in the superelastic responses of SMAs at micro-and nanoscales. For instance, the CuAlNi microwires and submicron pillars show a substantially higher capacity for the energy dissipation than that of bulk samples, which offers a significant promise for the applications in protective materials.In this thesis, a continuum model is developed in order to improve our understanding of size effects in SMAs at small scales. The modeling approach combines classic superelastic models, which use the volume fraction as an internal variable to represent the martensitic phase transformation, with strain gradient plasticity theories. Size effects are incorporated through two internal length scales, an energetic length scale and a dissipative length scale, which correspond to the martensitic volume fraction gradient and its time rate of change, respectively. Introducing the gradient of the martensitic volume fraction leads to coupled macro-and microforce balance equations, where the displacements and the martensitic volume fraction are both independent fields. A variational formulation for the temporally-discretized coupled macro-and microforce balance equations is proposed, as well as a computational framework based on this formulation. A robust and scalable parallel algorithm is implemented within this computational framework, which enables the large-scale three-dimensional study of size effects in SMAs with unprecedented resolution. This modeling and computational framework furnishes, in effect, a versatile tool to analyze a broad range of problems involving size effects in superelasticity with the potential to guide microstructure design and optimization. In particular, the model captures the increase of the stress hysteresis and strain hardening in bulk polycrystalline SMAs for decreasing grain size, as well as the increase of the residual strain for decreasing pillar size in NiTi pillars. The model confirms that constraints like grain boundaries 3 and the surface Ti oxide layer are responsible for the size-dependent superelasticity in SMAs.

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“…(12). The strategy to determine the peak value of the total kinetic energy and when it occurs is as follows:…”

Section: Figure 1 Ndfem Form-finding Processmentioning

confidence: 99%

“…(3) The dynamic relaxation method can be used in the form-finding and load analysis of tension structures [7][8][9][10][11][12]. This method converts the static problem into a dynamic problem using a virtual mass and a viscous damping force.…”

Section: Introductionmentioning

confidence: 99%

Static Equilibrium Form-Finding Analysis of Cable-Strut System Based on Nonlinear Dynamic Finite Element Method

Luo¹,

Zhang²,

Chen³

et al. 2015

Volume 11 Number 4

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ABSTRACT:Full tensile structures (such as cable domes, cable networks and cable trusses) are structures that only consist of cables and struts. There are three steps in its onsite construction: (1) assembly and connection, (2) towing and lifting and (3) tensioning and shaping. During construction process, the structure may suffer from large mechanism displacement and cable slack, so its initial shape was far from equilibrium. The form-finding analysis is a major difficulty in the construction process analysis. In this paper, we propose a new method for static equilibrium form-finding analysis of a cable-strut system based on a nonlinear dynamic finite element method and introduce virtual inertia and viscous damping force, as well as a series analysis techniques and a multi-step continuous solver. When the total system kinetic energy reaches its peak, the finite element model is updated, and the dynamic equilibria gradually converge to a static equilibrium state through iterative updating. To improve the analysis efficiency, stability and accuracy, key technical measures are proposed for time-step lengths, total energy peak value, model updating, convergence criteria and static equilibrium verification. In the case of the rigid cable dome in Wuxi New District Science and Technology Exchange Centre in China, we used this method to perform the mechanical analysis during the integral tow-lifting and tensioning process, and the project corresponded with our analysis. Meanwhile, we have to mention that during the construction process of integral tow-lifting, an inflection point exists in the adjustment phase, at which point the configuration stability is the worst and struts can fall sideways. Especially, for cable domes with a high rise-span ratio, the stability at the inflection point needs to be addressed.

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Adaptive dynamic relaxation algorithm for non-linear hyperelastic structures Part I. Formulation

Cited by 76 publications

References 33 publications

Structural Design of a Practical Large-Span Cable-Frame Type of Suspended Single-Layer Reticulated Shell With Free Surface

Structural Design of a Practical Large-Span Cable-Frame Type of Suspended Single-Layer Reticulated Shell With Free Surface

Computational modeling of size-dependent superelasticity of shape memory alloys

Static Equilibrium Form-Finding Analysis of Cable-Strut System Based on Nonlinear Dynamic Finite Element Method

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