☆ 4.7 Article

Residual-based error corrector operator to enhance accuracy and reliability of neural operator surrogates of nonlinear variational boundary-value problems

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2024)

相关参考文献

注意：仅列出部分参考文献，下载原文获取全部文献信息。

Article Materials Science, Multidisciplinary

Theory of hard magnetic soft materials to create magnetoelectricity

Amir Hossein Rahmati et al.

Summary: Magnetoelectrics are materials that can generate electrical signals wirelessly. However, achieving this effect in natural materials or artificial composites has been challenging. In this study, we propose a theoretical framework and demonstrate its effectiveness in understanding and designing soft magnetoelectric materials. Our theory shows that mechanical strain can induce a strong magnetoelectric coupling, independent of external magnetic fields, even at low frequencies.

JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS (2023)

添加到收藏夹

Article Materials Science, Multidisciplinary

High-dimensional nonlinear Bayesian inference of poroelastic fields from pressure data

Mina Karimi et al.

Summary: We explore the use of Bayesian inference for solving large-scale inverse problems governed by partial differential equations (PDEs). Markov Chain Monte Carlo (MCMC) methods are employed to generate samples and estimate posterior uncertainty. To improve efficiency in high-dimensional problems, the gradient and Hessian of the target potential are utilized through Hamiltonian Monte Carlo (HMC). Specifically, we apply this framework to infer the field of soil permeability from pore pressure observations using a nonlinear PDE poromechanics model. The performance of different sampling approaches, as well as the impact of dimensionality and non-Gaussian distributions, are studied.

MATHEMATICS AND MECHANICS OF SOLIDS (2023)

添加到收藏夹

Article Mathematics, Applied

SIMULATING GRAIN SHAPE EFFECTS AND DAMAGE IN GRANULAR MEDIA USING PERIDEM

Debdeep Bhattacharya et al.

Summary: We provide a numerical platform for analyzing the influence of particle shape and topology on the macroscopic behavior of granular media. Our approach combines the discrete element method (DEM) with a peridynamic model, which considers deformation and damage of individual particles. To handle arbitrary particle shapes and topology, we develop an efficient method for intraparticle peridynamic interaction within particle boundaries. We also improve accuracy by analytically computing particle contact with the rigid boundary wall. Additionally, we use an optimization-based method to speed up simulations with particles of different shapes and sizes, by choosing an initial configuration using security disks in a jammed state. The effect of particle shape and topology on settling and compaction of deformable particles in the aggregate is analyzed.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2023)

添加到收藏夹

Article Mathematics, Applied

Large-Scale Bayesian Optimal Experimental Design with Derivative-Informed Projected Neural Network

Keyi Wu et al.

Summary: This paper proposes a method for solving large-scale Bayesian optimal experimental design problems with partial differential equations as constraints and infinite-dimensional parameter fields. By replacing the PDE solve with a derivative-informed projected neural network, the problem is simplified to a process solved by a greedy algorithm, avoiding computationally intensive calculations.

JOURNAL OF SCIENTIFIC COMPUTING (2023)

添加到收藏夹

Review Engineering, Multidisciplinary

Operator inference for non-intrusive model reduction with quadratic manifolds

Rudy Geelen et al.

Summary: This paper proposes a novel approach for learning a quadratic manifold from high-dimensional data and using it to derive efficient physics-based reduced-order models. The approach involves a polynomial mapping between high-dimensional states and a low-dimensional embedding, consisting of a linear subspace representation and a quadratic component. This non-intrusive method combines the quadratic manifold approximation with projection-based model reduction for scalable learning of reduced-order models.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2023)

添加到收藏夹

Article Computer Science, Interdisciplinary Applications

Bayesian Inference of Tissue Heterogeneity for Individualized Prediction of Glioma Growth

Baoshan Liang et al.

Summary: This study introduces a Bayesian framework to reliably predict the future spread of brain tumors using MRI data. The framework calibrates the spatial distribution of tumor growth model parameters based on quantitative MRI measurements and leverages subject-specific priors and tunable spatial dependencies. Results show that the calibrated tumor model can accurately predict tumor shapes, but the reliability of predicted tumor volume and shape depends on the number of earlier imaging time points used for calibration.

IEEE TRANSACTIONS ON MEDICAL IMAGING (2023)

添加到收藏夹

Article Computer Science, Interdisciplinary Applications

Residual-based error correction for neural operator accelerated infinite-dimensional Bayesian inverse problems

Lianghao Cao et al.

Summary: This study explores the use of neural operators to accelerate infinite-dimensional Bayesian inverse problems with models governed by nonlinear parametric partial differential equations. While neural operators have the potential to drastically reduce computational costs, reducing approximation error in training can be challenging and unreliable. To address this, a strategy is proposed that corrects the prediction of trained neural operators by solving a linear variational problem based on the PDE residual, achieving improved accuracy without sacrificing computational speed.

JOURNAL OF COMPUTATIONAL PHYSICS (2023)

添加到收藏夹

Article Computer Science, Interdisciplinary Applications

Optimal design of chemoepitaxial guideposts for the directed self-assembly of block copolymer systems using an inexact Newton algorithm

Dingcheng Luo et al.

Summary: Directed self-assembly (DSA) of block copolymers (BCPs) is a promising method for cost-effective production of nanoscale devices. This paper presents a phase field model and a PDE-constrained optimization framework for the optimal design problem of substrate pattern for the DSA process. The computational strategy demonstrated significant improvement in computational cost and the optimization algorithm achieved fast convergence in both two and three spatial dimensions.

JOURNAL OF COMPUTATIONAL PHYSICS (2023)

添加到收藏夹

Article Engineering, Multidisciplinary

Data-driven physics-based digital twins via a library of component-based reduced-order models

M. G. Kapteyn et al.

Summary: This work proposes a method that combines a library of component-based reduced-order models with Bayesian state estimation to create data-driven physics-based digital twins. The approach successfully establishes reliable physics-based computational models and fast adaptability, demonstrating the development of a digital twin for an unmanned aerial vehicle.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2022)

添加到收藏夹

Article Engineering, Multidisciplinary

POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition

Stefania Fresca et al.

Summary: DL-ROMs are proposed to overcome limitations of conventional ROMs, but require expensive training. The proposed method combines POD and multi-fidelity pretraining to avoid the costly training stage of DL-ROMs.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2022)

添加到收藏夹

Article Engineering, Multidisciplinary

Derivative-informed projected neural networks for high-dimensional parametric maps governed by PDEs

Thomas O'Leary-Roseberry et al.

Summary: Many-query problems in various fields require evaluations of high-dimensional parametric maps governed by PDEs, which can be prohibitive. The proposed approach of derivative-informed projected neural networks captures the geometry and intrinsic low-dimensionality of these maps by training weights in low-dimensional layers. This method achieves greater generalization accuracy and independence of weight dimension on parametric and output dimensions.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2022)

添加到收藏夹

Article Mathematics, Applied

A GLOBALLY CONVERGENT MODIFIED NEWTON METHOD FOR THE DIRECT MINIMIZATION OF THE OHTA-KAWASAKI ENERGY WITH APPLICATION TO THE DIRECTED SELF-ASSEMBLY OF DIBLOCK COPOLYMERS

Lianghao Cao et al.

Summary: We propose a fast and robust scheme for minimizing the OhtaKawasaki energy of microphase separation in diblock copolymer melts. The scheme is shown to be significantly more efficient than the commonly used gradient flow approach, with mass-conservation, energy-descending, and asymptotic quadratic convergence properties.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2022)

添加到收藏夹

Article Water Resources

U-FNO-An enhanced Fourier neural operator-based deep-learning model for flow

Gege Wen et al.

Summary: Numerical simulation of multiphase flow plays a vital role in geoscience applications. The U-FNO neural network architecture, based on the Fourier neural operator (FNO), offers a superior and efficient solution for solving multiphase flow problems. It outperforms traditional simulators in accuracy, speed, and data utilization.

ADVANCES IN WATER RESOURCES (2022)

添加到收藏夹

Article Mathematics, Interdisciplinary Applications

A digital-twin and machine-learning framework for precise heat and energy management of data-centers

T. Zohdi

Summary: The massive growth in data centers has led to increased interest and regulations for waste heat management. This study aims to optimize ventilation and cooling in data centers using a combined Digital-Twin and Machine-Learning framework, resulting in a model problem and iterative solution method.

COMPUTATIONAL MECHANICS (2022)

添加到收藏夹

Article Engineering, Multidisciplinary

Gradient-enhanced physics-informed neural networks for forward and inverse PDE

Jeremy Yu et al.

Summary: The article introduces a new method called gradient-enhanced physics-informed neural networks (gPINNs) to improve the accuracy of PINNs. gPINNs leverage the gradient information of the PDE residual to enhance the loss function. Experimental results demonstrate that gPINNs outperform traditional PINN with fewer training points.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2022)

添加到收藏夹

Review Physics, Multidisciplinary

Coupling of mechanical deformation and electromagnetic fields in biological cells

Mehdi Torbati et al.

Summary: The cell, as the fundamental unit of life, exhibits complex emergent behavior that is influenced by mechanical and electromagnetic forces. Understanding the mechanics of cells is important in determining biological functions and has applications in medical research.

REVIEWS OF MODERN PHYSICS (2022)

添加到收藏夹

Article Computer Science, Interdisciplinary Applications

A level set-based topology optimization approach for thermally radiating structures

Brian S. Cohen et al.

Summary: This paper introduces a level-set based topology optimization approach for designing thermally efficient radiating structures. The authors derive the shape sensitivity using the adjoint method and apply gradient-based algorithm and augmented Lagrangian method to solve the problem of maximizing heat power. A case study demonstrates that maximizing the thermal compliance functional is insufficient for solving this type of problem.

STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION (2022)

添加到收藏夹

Article Computer Science, Interdisciplinary Applications

Goal-oriented a-posteriori estimation of model error as an aid to parameter estimation

Prashant K. Jha et al.

Summary: This work presents a Bayesian model calibration framework that uses goal-oriented a-posterior error estimates in quantities of interest (QoIs) to calibrate high-fidelity models characterized by PDEs. The framework allows for computationally inexpensive calibration of high-fidelity models when parameters of low-fidelity surrogate models are known accurately. The approach involves estimating the error in QoIs using a lower fidelity model, and using these estimates to define likelihood functions for Bayesian inversion analysis.

JOURNAL OF COMPUTATIONAL PHYSICS (2022)

添加到收藏夹

Article Mathematics, Applied

REDUCED OPERATOR INFERENCE FOR NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

Elizabeth Qian et al.

Summary: We propose a new scientific machine learning method that learns from data to predict the evolution of a system governed by a time-dependent nonlinear partial differential equation. The method combines projection-based model reduction with supervised machine learning tools to reduce the computational cost of the model, achieving accurate predictions in test cases.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2022)

添加到收藏夹

Article Engineering, Multidisciplinary

Learning high-dimensional parametric maps via reduced basis adaptive residual networks

Thomas O'Leary-Roseberry et al.

Summary: This article proposes a scalable framework for learning high-dimensional parametric maps using adaptively constructed residual network (ResNet) maps. By linearly restricting high-dimensional maps to informed reduced bases of the inputs, the ill-posedness of the neural network training problem can be ameliorated. Inspired by recent approximation theory, the article presents an adaptive ResNet construction algorithm that allows for depth-wise enrichment of the neural network approximation. The proposed methodology achieves remarkably high accuracy for limited training data.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2022)

添加到收藏夹

Article Computer Science, Interdisciplinary Applications

Direct lagrange multiplier updates in topology optimization revisited

Tej Kumar et al.

Summary: This paper introduces a direct method for computing Lagrange multipliers in topology optimization. Through benchmark problems, it demonstrates advantages over the traditional bisection method including fewer and faster update iterations, smoother and more robust convergence, and insensitivity to material and force parameters. The method also provides drop-in replacements for popular Matlab-based topology optimization codes.

STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION (2021)

添加到收藏夹

Article Engineering, Multidisciplinary

Modeling and simulation of vascular tumors embedded in evolving capillary networks

Marvin Fritz et al.

Summary: This work presents a coupled 3D-1D model for realistic simulations of tumor growth and angiogenesis in a dynamically changing vascular network, incorporating erosion of the extracellular matrix, interstitial flow, and coupled flow in blood vessels and tissue. The evolution of the blood vessel network is controlled by the concentration of tumor angiogenesis factors, allowing for random growth and stochastic tumor development. The model demonstrates flexibility in generating satellite tumors and simulating the effects of angiogenesis on tumor growth, as well as sample-independent features of cancer.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2021)

添加到收藏夹

Article Computer Science, Interdisciplinary Applications

Optimal design of acoustic metamaterial cloaks under uncertainty

Peng Chen et al.

Summary: This study focuses on the optimal design of an acoustic cloak under uncertainty and develops scalable approximation and optimization methods to solve this problem. Numerical experiments demonstrate the scalability of the method with respect to the dimensions of design variables and uncertain parameters.

JOURNAL OF COMPUTATIONAL PHYSICS (2021)

添加到收藏夹

Article Mathematics, Applied

Analysis of a new multispecies tumor growth model coupling 3D phase-fields with a 1D vascular network

Marvin Fritz et al.

Summary: This work presents and analyzes a mathematical model for tumor growth that incorporates ECM erosion, interstitial flow, vascular flow, and nutrient transport. The model is phase-field or diffused-interface type with smooth evolving interfaces separating cell species and constituents. It uses a mesoscale version of Darcy's law to capture flow mechanisms in tissue matrix, and considers 1D equations for flow and transport processes in the vasculature. The models for transport, flow, and cell species define a 3D-1D coupled model.

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS (2021)

添加到收藏夹

Article Multidisciplinary Sciences

Learning the solution operator of parametric partial differential equations with physics-informed DeepONets

Sifan Wang et al.

Summary: The physics-informed DeepONets framework can effectively learn the solution operator of arbitrary PDEs even in the absence of paired training data. It is able to predict the solution of various parametric PDEs up to three orders of magnitude faster compared to conventional solvers, setting a new paradigm for modeling and simulation of nonlinear and nonequilibrium processes in science and engineering.

SCIENCE ADVANCES (2021)

添加到收藏夹

Article Engineering, Multidisciplinary

A monolithic arbitrary Lagrangian-Eulerian-based finite element strategy for fluid-structure interaction problems involving a compressible fluid

Suman Dutta et al.

Summary: A new monolithic finite element strategy is proposed for solving fluid-structure interaction problems involving a compressible fluid and a hyperelastic structure. The strategy conserves total energy and linear and angular momenta, while ensuring stability and efficiency through detailed numerical validations. The use of exact tangent stiffness matrix allows the algorithm to converge quadratically within each time step, with benchmark examples illustrating the method's good performance.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2021)

添加到收藏夹

Article Materials Science, Multidisciplinary

Peridynamics-based discrete element method (PeriDEM) model of granular systems involving breakage of arbitrarily shaped particles

Prashant K. Jha et al.

Summary: The study introduces a hybrid model called PeriDEM, which combines peridynamics and DEM to improve the performance and efficiency of engineering systems involving granular or particulate media. The model can simulate arbitrarily shaped particles and investigates the effect of mesh resolution on intraparticle peridynamics.

JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS (2021)

添加到收藏夹

Article Computer Science, Artificial Intelligence

Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

Lu Lu et al.

Summary: This study extends the capabilities of neural networks with the introduction of the deep operator network (DeepONet), which can be used to learn various operators, including explicit and implicit operators. Different formulations of the input function space were studied and their effect on generalization error for 16 diverse applications was examined.

NATURE MACHINE INTELLIGENCE (2021)

添加到收藏夹

Article Engineering, Mechanical

Transfer learning enhanced physics informed neural network for phase-field modeling of fracture

Somdatta Goswami et al.

THEORETICAL AND APPLIED FRACTURE MECHANICS (2020)

添加到收藏夹

Article Mathematics, Interdisciplinary Applications

Bayesian-based predictions of COVID-19 evolution in Texas using multispecies mixture-theoretic continuum models

Prashant K. Jha et al.

COMPUTATIONAL MECHANICS (2020)

添加到收藏夹

Article Materials Science, Multidisciplinary

Kinetic relations and local energy balance for LEFM from a nonlocal peridynamic model

Prashant K. Jha et al.

INTERNATIONAL JOURNAL OF FRACTURE (2020)

添加到收藏夹

Article Computer Science, Interdisciplinary Applications

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

M. Raissi et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2019)

添加到收藏夹

Article Materials Science, Multidisciplinary

Mechanics of hard-magnetic soft materials

Ruike Zhao et al.

JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS (2019)

添加到收藏夹

Article Computer Science, Interdisciplinary Applications

Taylor approximation and variance reduction for PDE-constrained optimal control under uncertainty

Peng Chen et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2019)

添加到收藏夹

Article Chemistry, Physical

Designing soft pyroelectric and electrocaloric materials using electrets

Faezeh Darbaniyan et al.

SOFT MATTER (2019)

添加到收藏夹

Article Oncology

Mechanism-based Modeling of Tumor Growth and Treatment Response Constrained by Multiparametric Imaging Data

David A. Hormuth et al.

JCO CLINICAL CANCER INFORMATICS (2019)

添加到收藏夹

Article Computer Science, Interdisciplinary Applications

Non-intrusive reduced order modeling of nonlinear problems using neural networks

J. S. Hesthaven et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2018)

添加到收藏夹

Article Engineering, Multidisciplinary

Free Damage Propagation with Memory

Robert Lipton et al.

JOURNAL OF ELASTICITY (2018)

添加到收藏夹

Article Materials Science, Multidisciplinary

Bond-level deformation gradients and energy averaging in peridynamics

Timothy Breitzman et al.

JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS (2018)

添加到收藏夹

Article Mathematics, Applied

NUMERICAL ANALYSIS OF NONLOCAL FRACTURE MODELS IN HOLDER SPACE

Prashant K. Jha et al.

SIAM JOURNAL ON NUMERICAL ANALYSIS (2018)

添加到收藏夹

Article Mathematics

Adaptive multiscale predictive modelling

J. Tinsley Oden

ACTA NUMERICA (2018)

添加到收藏夹

Article Engineering, Multidisciplinary

A monolithic finite-element formulation for magnetohydrodynamics

Arup Nandy et al.

SADHANA-ACADEMY PROCEEDINGS IN ENGINEERING SCIENCES (2018)

添加到收藏夹

Article Mathematics, Interdisciplinary Applications

Mean-Variance Risk-Averse Optimal Control of Systems Governed by PDEs with Random Parameter Fields Using Quadratic Approximations

Alen Alexanderian et al.

SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION (2017)

添加到收藏夹

Article Engineering, Multidisciplinary

Selection and validation of predictive models of radiation effects on tumor growth based on noninvasive imaging data

E. A. B. F. Lima et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2017)

添加到收藏夹

Review Computer Science, Interdisciplinary Applications

Toward Predictive Multiscale Modeling of Vascular Tumor Growth

J. Tinsley Oden et al.

ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING (2016)

添加到收藏夹

Article Mathematics, Applied

Selection, calibration, and validation of models of tumor growth

E. A. B. F. Lima et al.

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES (2016)

添加到收藏夹

Article Computer Science, Software Engineering

Unified Form Language: A Domain-Specific Language for Weak Formulations of Partial Differential Equations

Martin S. Alnaes et al.

ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE (2014)

添加到收藏夹

Article Mathematics, Applied

A COMPUTATIONAL FRAMEWORK FOR INFINITE-DIMENSIONAL BAYESIAN INVERSE PROBLEMS, PART II: STOCHASTIC NEWTON MCMC WITH APPLICATION TO ICE SHEET FLOW INVERSE PROBLEMS

Noemi Petra et al.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2014)

添加到收藏夹

Article Computer Science, Interdisciplinary Applications

Simulation-based optimal Bayesian experimental design for nonlinear systems

Xun Huan et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2013)

添加到收藏夹

Article Biology

Bayesian calibration, validation, and uncertainty quantification of diffuse interface models of tumor growth

Andrea Hawkins-Daarud et al.

JOURNAL OF MATHEMATICAL BIOLOGY (2013)

添加到收藏夹

Article Mathematics, Applied

ON THE NEWTON-KANTOROVICH THEOREM

Philippe G. Ciarlet et al.

ANALYSIS AND APPLICATIONS (2012)

添加到收藏夹

Article Computer Science, Interdisciplinary Applications

Optimization of vibrating structures to reduce radiated noise

Arup Kumar Nandy et al.

STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION (2012)

添加到收藏夹

Article Mathematics, Applied

Goal-Oriented Error Estimation for Cahn-Hilliard Models of Binary Phase Transition

Kristoffer G. van der Zee et al.

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS (2011)

添加到收藏夹

Article Mathematics, Applied

GENERAL DIFFUSE-INTERFACE THEORIES AND AN APPROACH TO PREDICTIVE TUMOR GROWTH MODELING

J. Tinsley Oden et al.

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES (2010)

添加到收藏夹

Article Engineering, Multidisciplinary

Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities

Christophe Geuzaine et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2009)

添加到收藏夹

Article Computer Science, Interdisciplinary Applications

Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems

Youssef M. Marzouk et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2009)

添加到收藏夹

Article Engineering, Multidisciplinary

An efficient reduced-order modeling approach for non-linear parametrized partial differential equations

N. C. Nguyen et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2008)

添加到收藏夹

Article Materials Science, Multidisciplinary

Kinetics of phase transformations in the peridynamic formulation of continuum mechanics

Kaushik Dayal et al.

JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS (2006)

添加到收藏夹

Article Computer Science, Interdisciplinary Applications

Estimation of modeling error in computational mechanics

JT Oden et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2002)

添加到收藏夹

Article Acoustics

Topology design of stpuctures subjected to periodic loading

CS Jog

JOURNAL OF SOUND AND VIBRATION (2002)

添加到收藏夹

Article Mechanics

Design of functionally graded composite structures in the presence of stress constraints

R Lipton

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES (2002)

添加到收藏夹

Article Mathematics, Applied

Goal-oriented error estimation and adaptivity for the finite element method

JT Oden et al.

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2001)

添加到收藏夹

© Peeref 2019-2024. All rights reserved.