查看更多>>摘要：Abstract An important property of implicit time integration algorithms for structural dynamics is their tendency to “overshoot” the exact solution in the first few steps of the computed response due to high‐frequency components in the initial excitations. The typical analysis technique for overshooting involves the study of asymptotic response of the algorithm's first step in the limiting high frequency case. This article finds that the prior analysis of overshooting in much of the engineering literature is incomplete in that it neglects the effect of physical damping. With physical damping included, first‐order overshooting components enter into several well‐known time integration algorithms which were previously thought to exhibit zero‐order overshooting in displacement. The Newmark method, Wilson‐θ method, Bazzi‐ρ method, HHT‐α method, WBZ‐α method, and three parameter optimal/generalized‐α method are analyzed, as well as the generalized single‐step single‐solve (GSSSS) framework which encompasses all of the prior schemes and other new and optimal algorithms and designs based upon the issues under consideration. The additional overshooting component is eliminated in the novel amended GSSSS V0 family (which is noteworthy and cannot be derived by conventional means), while the numerically dissipative schemes in the GSSSS U0 family (encompassing traditional methods such as the HHT‐α method, WBZ‐α method, and three parameter optimal/generalized‐α method among other new algorithm designs) are shown to be irremediable as the additional overshooting component from physical damping enters into the second step of the response, which is a wholly new finding. Numerical verifications of the overshooting analysis are performed for SDOF and MDOF structures with and without physical damping, and practical recommendations are given for the solution of MDOF problems on the basis of algorithm design and selection for various initial conditions.
查看更多>>摘要：Abstract This article introduces a new additional test concept and numerical property of implicit time integration methods termed as “aliasing” of the external load which must be considered during the algorithm design process. Where most numerical properties of such algorithms discussed in the literature pertain to the homogeneous components, aliasing reflects the tendency of the nonhomogeneous components to introduce errors into the solution in the asymptotic high‐frequency limit. An analytical technique is proposed to detect and quantify aliasing, defined in terms of the resulting representative solution. A theorem establishes whether a representative solution with aliasing can be bounded up to a constant by the external force values and thus treated as acceptable if the bound is sufficiently small. For the U0 family of algorithms within the GSSSS‐II framework containing several traditional and closely related methods, this is not an issue. However, the numerically dissipative GSSSS‐II V0 family of methods is shown to exhibit bounded aliasing with a constant roughly equal to 2, while the “structure‐dependent” Chang Family Method is shown to exhibit unbounded aliasing, which is not acceptable for practical dynamic computations. Numerical verifications are performed with single‐degree and multi‐degree of freedom problems with a series of selected algorithms which exhibit either no aliasing, tightly bounded aliasing, unbounded aliasing, or large bounded aliasing, and practical recommendations are given for acceptable aliasing of the load with special emphasis on MDOF problems such as those arising from finite element discretizations.
查看更多>>摘要：Abstract A mechanics‐informed artificial neural network approach for learning constitutive laws governing complex, nonlinear, elastic materials from strain–stress data is proposed. The approach features a robust and accurate method for training a regression‐based model capable of capturing highly nonlinear strain–stress mappings, while preserving some fundamental principles of solid mechanics. In this sense, it is a structure‐preserving approach for constructing a data‐driven model featuring both the form‐agnostic advantage of purely phenomenological data‐driven regressions and the physical soundness of mechanistic models. The proposed methodology enforces desirable mathematical properties on the network architecture to guarantee the satisfaction of physical constraints such as objectivity, consistency (preservation of rigid body modes), dynamic stability, and material stability, which are important for successfully exploiting the resulting model in numerical simulations. Indeed, embedding such notions in a learning approach reduces a model's sensitivity to noise and promotes its robustness to inputs outside the training domain. The merits of the proposed learning approach are highlighted using several finite element analysis examples. Its potential for ensuring the computational tractability of multi‐scale applications is demonstrated with the acceleration of the nonlinear, dynamic, multi‐scale, fluid‐structure simulation of the supersonic inflation dynamics of a parachute system with a canopy made of a woven fabric.
Alex A. GorodetskyDoug AllaireJohn D. JakemanSam Friedman...
31页
查看更多>>摘要：Abstract We present an adaptive algorithm for constructing surrogate models of multi‐disciplinary systems composed of a set of coupled components. With this goal we introduce “coupling” variables with a priori unknown distributions that allow surrogates of each component to be built independently. Once built, the surrogates of the components are combined to form an integrated‐surrogate that can be used to predict system‐level quantities of interest at a fraction of the cost of the original model. The error in the integrated‐surrogate is greedily minimized using an experimental design procedure that allocates the amount of training data, used to construct each component‐surrogate, based on the contribution of those surrogates to the error of the integrated‐surrogate. The multi‐fidelity procedure presented is a generalization of multi‐index stochastic collocation that can leverage ensembles of models of varying cost and accuracy, for one or more components, to reduce the computational cost of constructing the integrated‐surrogate. Extensive numerical results demonstrate that, for a fixed computational budget, our algorithm is able to produce surrogates that are orders of magnitude more accurate than methods that treat the integrated system as a black‐box.
查看更多>>摘要：Abstract Aircraft composite parts are commonly manufactured from resin‐saturated thermoset pre‐impregnated plies laid‐up over a rigid tool and consolidated and cured in an autoclave. In many applications, autoclave consolidation alone is not sufficient to remove the air, or bulk, that has been entrapped within the laminate during layup. Entrapped bulk can lead to the formation of defects, including wrinkles and voids, which can significantly affect structural performance. Vacuum consolidation, or “debulking,” has been a standard practice extensively used by aircraft manufacturers to reduce the amount of bulk and mitigate defect formation. Yet, the underlying physical principles governing formation of defects during these early stages are not well understood. This work presents the development of a new finite element‐based method for simulation of debulking with the objective to contribute to a better understanding of the key physics involved. The model includes pore‐pressure cohesive elements inserted at ply interfaces for discrete representation of entrapped air pockets and modeling air flow during debulking; and cohesive contact between the plies for simulating the typical tacky behavior of uncured thermoset tape prepregs. The debulking of a two‐ply laminate with an initial seeded wrinkle is considered for illustration of the approach and comparison with experimental results.
查看更多>>摘要：Abstract The formation mechanism of residual stress on the machined surface of belt grinding is sophisticated, and residual stress is an important factor affecting the fatigue life of aero‐engine blades. In this study, a prediction model of residual stress in a belt grinding blade is proposed with the geometrical characteristics and progressive wear of the grains as the research topic. By extracting the morphological features of abrasive belt, the residual stress based on different geometrical characteristics of grains (pyramidal, hexahedral, spherical, and conical belts) were investigated, and the optimal grain geometry was determined to be a uniformly arranged positive quadrilateral cone. Accordingly, a grinding experiment with a pyramidal belt was conducted to obtain an experienced model of the grain wear height. A numerical simulation model of the grain wear evolution under four wear states (no abrasion, early abrasion, middle abrasion, and late abrasion) was developed. Additionally, more detailed progressive wear of the abrasive grains was also applied to grind the entire profile of the complex curved blade. The residual stress on the blade surface was mainly compressive, and the surface stress values were distributed between ?385 and ?117?MPa with the service life of the pyramidal abrasive belt.
查看更多>>摘要：Abstract In this article, we formulate and implement a computational multiphase periporomechanics paradigm for unguided fracturing in unsaturated porous media assuming passive pore air pressure. The same governing equation for the solid phase applies on and off cracks. Crack formation in this framework is autonomous, requiring no prior estimates of crack topology. As a new contribution, an energy‐based criterion for arbitrary crack formation is formulated using the peridynamic effective force state for unsaturated porous media. Unsaturated fluid flow in the fracture space is modeled in a simplified way in line with the nonlocal formulation of unsaturated fluid flow in the bulk. The formulated unsaturated fracturing periporomechanics is numerically implemented through an implicit fractional step algorithm in time and a two‐phase mixed meshless method in space. The two‐stage operator split converts the coupled periporomechanics problem into an undrained deformation and fracture problem and an unsaturated fluid flow in the deformed skeleton configuration. Numerical simulations of in‐plane open and shear cracking are conducted to validate the accuracy and robustness of the fracturing unsaturated periporomechanics model. Then numerical examples of wing cracking and nonplanar cracking in unsaturated soil specimens are presented to demonstrate the efficacy of the proposed multiphase periporomechanics paradigm for unguided cracking in unsaturated porous media.
查看更多>>摘要：Abstract This study presents a scalable three‐dimensional (3D) multiscale framework for continuum‐discrete modeling of granular materials. The proposed framework features rigorous coupling of a continuum‐based material point method (MPM) and a discrete approach discrete element method (DEM) to enable cross‐scale modeling of boundary value problems pertaining to granular media. It employs MPM to solve the governing equations of a macroscopic continuum domain for a boundary value problem that may undergo large deformation. The required loading‐path‐dependent constitutive responses at each material point of the MPM are provided by a DEM solution based on grain‐scale contact‐based discrete simulations that receive macroscopic information at the specific material point as boundary conditions. This hierarchical coupling enables direct dialogs between the macro and micro scales of granular media while fully harnessing the predictive advantages of both MPM and DEM at the two scales. An effective, scalable parallel scheme is further developed, based on the flat message passing interface (MPI) model, to address the computational cost of the proposed framework for 3D large‐scale simulations. We demonstrate that the proposed parallel scheme may offer up to 32X and 40X speedup in strong and weak scaling tests, respectively, significantly empowering the numerical performance and predictive capability of the proposed framework. The 3D parallelized multiscale framework is validated by an element test and a column collapse problem, before being applied to simulate the intrusion of a solid object. The multiscale simulation successfully captures the characteristic response of intrusion as postulated by the modified Archimedes' law theory. The progressive development of the stagnant zone during the intrusion is further examined from a cross‐scale perspective.
查看更多>>摘要：Abstract We propose a projection‐based monolithic model order reduction procedure for a class of problems in nonlinear mechanics with internal variables. The work is motivated by applications to thermo‐hydro‐mechanical (THM) systems for radioactive waste disposal. THM equations model the behavior of temperature, pore water pressure, and solid displacement in the neighborhood of geological repositories, which contain radioactive waste and are responsible for a significant thermal flux toward the Earth's surface. We develop an adaptive sampling strategy based on the POD‐Greedy method, and we develop an element‐wise empirical quadrature hyper‐reduction procedure to reduce assembling costs. We present numerical results for a two‐dimensional THM system to illustrate and validate the proposed methodology.
NSTL
Wiley