Structural Mechanics

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Overview

Structural mechanics studies how solids, beams, shells, lattices, and other structures deform, carry loads, vibrate, buckle, and fail, linking material behavior and geometry to safety and design. Work combines finite-element and variational methods with experiments, while reduced-order models, physics-informed networks, graph neural networks, and neural operators aim to predict stress fields and dynamic responses at lower cost. These approaches address nonlinear elasticity, composites, fracture and contact, crash behavior, architected materials, and inverse tasks such as identifying loads or defects; topology and reliability-based optimization use them to find designs under constraints and uncertainty. A central challenge is preserving physical consistency while generalizing to new geometries, meshes, materials, and loading histories, and validating predictions against high-fidelity simulations and experiments.

Latest papers

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71 papers5 papers in the last four weeks, down 37% on the four weeks before. 0.0% of all new papers.

Mar 18, 2026

Symmetry-Reduced Physics-Informed Learning of Tensegrity Dynamics

Tensegrity structures possess intrinsic geometric symmetries that govern their dynamic behavior. However, most existing physics-informed neural network (PINN) approaches for tensegrity dynamics do not explicitly exploit these symmetries, leading to high computational complexity and unstable optimization. In this work, we propose a symmetry-reduced physics-informed neural network (SymPINN) framework that embeds group-theory-based symmetry directly into both the solution expression and the neural network architecture to predict tensegrity dynamics. By decomposing nodes into symmetry orbits and representing free nodal coordinates using a symmetry basis, the proposed method constructs a reduced coordinate representation that preserves geometric symmetry of the structure. The full coordinates are then recovered via symmetry transformations of the reduced solution learned by the network, ensuring that the predicted configurations automatically satisfy the symmetry constraints. In this framework, equivariance is enforced through orbit-based coordinate generation, symmetry-consistent message passing, and physics residual constraints. In addition, SymPINN improves training effectiveness by encoding initial conditions as hard constraints, incorporating Fourier feature encoding to enhance the representation of dynamic motions, and employing a two-stage optimization strategy. Extensive numerical experiments on symmetric T-bars and lander structures demonstrate significantly improved prediction accuracy and computational efficiency compared to standard physics-informed models, indicating the great potential of symmetry-aware learning for structure-preserving modeling of tensegrity dynamics.

Jing Qin, Muhao Chen

Department of Mathematics, University of Kentucky, Lexington, KY · Department of Mechanical and Aerospace Engineering, University of Houston, TX

Physics-Informed MLStructural MechanicsMultibody Dynamics
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Mar 18, 2026

Data-driven model order reduction for structures with piecewise linear nonlinearity using dynamic mode decomposition

Piecewise-linear nonlinear systems appear in many engineering disciplines. Prediction of the dynamic behavior of such systems is of great importance from practical and theoretical viewpoint. In this paper, a data-driven model order reduction method for piecewise-linear systems is proposed, which is based on dynamic mode decomposition (DMD). The overview of the concept of DMD is provided, and its application to model order reduction for nonlinear systems based on Galerkin projection is explained. The proposed approach uses impulse responses of the system to obtain snapshots of the state variables. The snapshots are then used to extract the dynamic modes that are used to form the projection basis vectors. The dynamics described by the equations of motion of the original full-order system are then projected onto the subspace spanned by the basis vectors. This produces a system with much smaller number of degrees of freedom (DOFs). The proposed method is applied to two representative examples of piecewise linear systems: a cantilevered beam subjected to an elastic stop at its end, and a bonded plates assembly with partial debonding. The reduced order models (ROMs) of these systems are constructed by using the Galerkin projection of the equation of motion with DMD modes alone, or DMD modes with a set of classical constraint modes to be able to handle the contact nonlinearity efficiently. The obtained ROMs are used for the nonlinear forced response analysis of the systems under harmonic loading. It is shown that the ROMs constructed by the proposed method produce accurate forced response results.

Akira Saito, Masato Tanaka

Department of Mechanical Engineering, Meiji University, Kawasaki, Kanagawa 214-8571, Japan. · Toyota Research Institute of North America Toyota Motor North America, Inc. Ann Arbor, Michigan, 48105, USA

Reduced-Order ModelingDynamical SystemsStructural Mechanics
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Mar 12, 2026

Deep Learning-Based Metamodeling of Nonlinear Stochastic Dynamic Systems under Parametric and Predictive Uncertainty

Modeling high-dimensional, nonlinear dynamic structural systems under natural hazards presents formidable computational challenges, especially when simultaneously accounting for uncertainties in external loads and structural parameters. Studies have successfully incorporated uncertainties related to external loads from natural hazards, but few have simultaneously addressed loading and parameter uncertainties within structural systems while accounting for prediction uncertainty of neural networks. To address these gaps, three metamodeling frameworks were formulated, each coupling a feature-extraction module implemented through a multi-layer perceptron (MLP), a message-passing neural network (MPNN), or an autoencoder (AE) with a long short-term memory (LSTM) network using Monte Carlo dropout and a negative log-likelihood loss. The resulting architectures (MLP-LSTM, MPNN-LSTM, and AE-LSTM) were validated on two case studies: a multi-degree-of-freedom Bouc-Wen system and a 37-story fiber-discretized nonlinear steel moment-resisting frame, both subjected to stochastic seismic excitation and structural parameter uncertainty. All three approaches achieved low prediction errors: the MLP-LSTM yielded the most accurate results for the lower-dimensional Bouc-Wen system, whereas the MPNN-LSTM and AE-LSTM provided superior performance on the more complex steel-frame model. Moreover, a consistent correlation between predictive variance and actual error confirms the suitability of these frameworks for active-learning strategies and for assessing model confidence in structural response predictions.

Haimiti Atila, Seymour M. J. Spence

Department of Civil and Environmental Engineering, University of Michigan, Ann Arbor, MI 48109, USA

Neural Surrogate ModelingUncertainty QuantificationStructural Mechanics
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Mar 10, 2026

A neural operator for predicting vibration frequency response curves from limited data

In the design of engineered components, rigorous vibration testing is essential for performance validation and identification of resonant frequencies and amplitudes encountered during operation. Performing this evaluation numerically via machine learning has great potential to accelerate design iteration and make testing workflows more efficient. However, dynamical systems are conventionally difficult to solve via machine learning methods without using physics-based regularizing loss functions. To properly perform this forecasting task, a structure that has an inspectable physical obedience can be devised without the use of regularizing terms from first principles. The method employed in this work is a neural operator integrated with an implicit numerical scheme. This architecture enables operators to learn of the underlying state-space dynamics from limited data, allowing generalization to untested driving frequencies and initial conditions. This network can infer the system's global frequency response by training on a small set of input conditions. As a foundational proof of concept, this investigation verifies the machine learning algorithm with a linear, single-degree-of-freedom system, demonstrating implicit obedience of dynamics. This approach demonstrates 99.87% accuracy in predicting the Frequency Response Curve (FRC), forecasting the frequency and amplitude of linear resonance training on 7% of the bandwidth of the solution. By training machine learning models to internalize physics information rather than trajectory, better generalization accuracy can be realized, vastly improving the timeframe for vibration studies on engineered components.

D. Bluedorn, A. Badawy, B. E. Saunders +2

Department of Mechanical and Aerospace Engineering, New Mexico State University, Las Cruces, NM 88003, USA. · Knight Foundation School of Computing and Information Science, Florida International University, Miami, FL 33199, USA. · Sandia National Laboratories, Albuquerque, NM 87123, USA.

Neural Surrogate ModelingNeural OperatorsStructural MechanicsSystem Identification
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Mar 7, 2026

A Dual-Graph Spatiotemporal GNN Surrogate for Nonlinear Response Prediction of Reinforced Concrete Beams under Four-Point Bending

High-fidelity nonlinear finite-element (FE) simulations of reinforced-concrete (RC) structures are still costly, especially in parametric settings where loading positions vary. We develop a dual-graph spatiotemporal GNN surrogate to approximate the time histories of RC beams under four-point bending. To generate training data, we run a parametric Abaqus campaign that independently shifts the two loading blocks on a mesh-aligned grid and exports full-field responses at fixed normalized loading levels. The model rolls out autoregressively and jointly predicts nodal displacements, element wise von Mises stress, element-wise equivalent plastic strain (PEEQ), and the global vertical reaction force in a single multi-task setup. A key motivation is the peak loss introduced when element quantities are forced through node-based representations. We therefore couple node- and element-level dynamics using two recurrent graph branches: a node-level graph convolutional gated recurrent unit (GConvGRU) for kinematics and an element-level GConvGRU for history-dependent internal variables, with global force predicted through pooling on the element branch. In controlled ablations, removing the Element to Node to Element pathway improves peak-sensitive prediction in localized high-gradient stress/PEEQ regions without degrading global load displacement trends. After training, the surrogate produces full trajectories at a fraction of the cost of nonlinear FE, enabling faster parametric evaluation and design exploration.

Zhaoyang Ren, Qilin Li

Discipline of Computing, School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, Australia

Neural Surrogate ModelingSpatiotemporal GNNsStructural EngineeringStructural Mechanics
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Mar 6, 2026

Physics-Consistent Neural Networks for Learning Deformation and Director Fields in Microstructured Media with Loss-Based Validation Criteria

In this work, we study the mechanical behavior of solids with microstructure using the framework of Cosserat elasticity with a single unit director. This formulation captures the coupling between deformation and orientational fields that arises in many structured materials. To compute equilibrium configurations of such media, we develop two complementary computational approaches: a finite element formulation based on variational principles and a neural network-based solver that directly minimizes the total potential energy. The neural architecture is constructed to respect the fundamental kinematic structure of the theory. In particular, it enforces frame invariance of the energy, satisfies the unit-length constraint on the director field, and represents deformation and director fields through separate networks to preserve their kinematic independence in the variational setting. Beyond satisfying balance laws, however, physically admissible solutions must also correspond to stable energy minimizers. To assess this requirement, we derive the quasiconvexity condition, rank-one convexity condition, and the Legendre-Hadamard inequalities for the Cosserat model and formulate them in a manner suitable for evaluating neural network predictions. These necessary stability conditions provide a physics-based validation framework: network outputs that violate these necessary conditions cannot correspond to stable energy minimizers and can therefore be rejected. In this way, we integrate classical variational stability theory with modern machine-learning solvers, establishing a computational workflow in which equilibrium solutions are not only learned but also assessed for energetic consistency.

Milad Shirani, Pete H. Gueldner, Murat Khidoyatov +2

Department of Biomedical Engineering, Yale University, New Haven, CT, USA · Department of Mechanical Engineering, Yale University, New Haven, CT, USA

Structural MechanicsMaterials ScienceNeural PDE Solvers
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Mar 5, 2026

Constraint-Free Static Modeling of Continuum Parallel Robot

Continuum parallel robots (CPR) combine rigid actuation mechanisms with multiple elastic rods in a closed-loop topology, making forward statics challenging when rigid--continuum junctions are enforced by explicit kinematic constraints. Such constraint-based formulations typically introduce additional algebraic variables and complicate both numerical solution and downstream control. This paper presents a geometric exact, configuration-based and constraint-free static model of CPR that remains valid under geometrically nonlinear, large-deformation and large-rotation conditions. Connectivity constraints are eliminated by kinematic embedding, yielding a reduced unconstrained problem. Each rod of CPR is discretized by nodal poses on SE(3), while the element-wise strain field is reconstructed through a linear strain parameterization. A fourth-order Magnus approximation yields an explicit and geometrically consistent mapping between element end poses and the strain. Rigid attachments at the motor-driven base and the end-effector platforms are handled through kinematic embeddings. Based on total potential energy and virtual work, we derive assembly-ready residuals and explicit Newton tangents, and solve the resulting nonlinear equilibrium equations using a Riemannian Newton iteration on the product manifold. Experiments on a three-servomotor, six-rod prototype validate the model by showing good agreement between simulation and measurements for both unloaded motions and externally loaded cases.

Lingxiao Xun, Matyas Diezinger, Azad Artinian +2

RoboticsStructural Mechanics
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Mar 3, 2026

Passive Phase-Oriented Impedance Shaping for Rapid Acceleration in Soft Robotic Swimmers

Rapid acceleration and burst maneuvers in underwater robots depend less on maintaining precise resonance and more on force--velocity phase alignment during thrust generation. In this work, we investigate constrained-layer damping (CLD) as a passive mechanism for frequency-selective impedance shaping in soft robotic swimmers. Unlike conventional stiffness-tuning approaches, CLD selectively amplifies the dissipative component of bending impedance while preserving storage stiffness, passively shifting the impedance composition toward dissipative dominance as actuation frequency increases. We characterize this behavior through dry impedance measurements, demonstrate that CLD enhances thrust and alters force--motion phase relationships across Strouhal numbers in constrained propulsion tests, and validate that passive impedance shaping yields a nearly five-fold increase in peak acceleration and a three-fold increase in terminal velocity in unconstrained swimming trials. These results establish phase-oriented passive impedance modulation as a simple, control-free pathway for improving transient propulsion in soft robotic systems.

Qimin Feng, Orion A. Roberts, Qiang Zhong

Department of Mechanical Engineering, Iowa State University, Ames, IA 50011, USA.

Robot LocomotionUnderwater RoboticsSoft RoboticsImpedance ControlStructural Mechanics
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Feb 25, 2026

Deep Clustering based Boundary-Decoder Net for Inter and Intra Layer Stress Prediction of Heterogeneous Integrated IC Chip

High stress occurs when 3D heterogeneous IC packages are subjected to thermal cycling at extreme temperatures. Stress mainly occurs at the interface between different materials. We investigate stress image using latent space representation which is based on using deep generative model (DGM). However, most DGM approaches are unsupervised, meaning they resort to image pairing (input and output) to train DGM. Instead, we rely on a recent boundary-decoder (BD) net, which uses boundary condition and image pairing for stress modeling. The boundary net maps material parameters to the latent space co-shared by its image counterpart. Because such a setup is dimensionally wise ill-posed, we further couple BD net with deep clustering. To access the performance of our proposed method, we simulate an IC chip dataset comprising of 1825 stress images. We compare our new approach using variants of BD net as well as a baseline approach. We show that our approach is able to outperform all the comparison in terms of train and test error reduction.

Kart Leong Lim, Ji Lin

Institute of Microelectronics (IME), Agency for Science, Technology and Research (A*STAR), 2 Fusionopolis Way, Innovis #08-02, Singapore 138634, Republic of Singapore

Neural Surrogate ModelingStructural Mechanics
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Dec 23, 2025

GeoTransolver: Learning Physics on Irregular Domains Using Multi-scale Geometry Aware Physics Attention Transformer

We present GeoTransolver, a multiscale geometry-aware physics attention transformer for Computer Aided Engineering (CAE). GeoTransolver extends the Transolver backbone with GALE (Geometry-Aware Latent Embeddings) attention, which pairs physics-aware self-attention on learned state slices with cross-attention to a shared geometry and global context computed via multi-scale ball queries (inspired by Domino) and reused in every block. Implemented and released in NVIDIA PhysicsNeMo, GeoTransolver persistently projects geometry and global parameters, into physical state spaces to anchor computations to domain structure and operating regimes. We benchmark on DrivAerML, SHIFT-SUV, and SHIFT-Wing against Domino, Transolver (PhysicsNeMo implementation), and literature-reported AB-UPT, evaluating drag/lift R2 and relative L1 errors on field variables. As an additional nonlinear structural mechanics application, we also report Transolver and GeoTransolver results on bumper-beam and full-vehicle Body-in-White (BIW) crash-dynamics benchmarks, evaluating relative L2 trajectory error and probe-level kinematic MSE. GeoTransolver delivers improved accuracy, robustness to geometry and regime shifts, and favorable data efficiency; we include DrivAerML ablations and qualitative contour and design-trend results, advancing operator learning for high-fidelity surrogates on complex, irregular, non-linear domains.

Corey Adams, Rishikesh Ranade, Ram Cherukuri +1

NVIDIA Corporation, Santa Clara, US

Neural Surrogate ModelingStructural MechanicsTransformer AttentionNeural OperatorsComputational Fluid Dynamics
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Jul 5, 2025

Physics-Informed Graph Neural Networks to Reconstruct Local Fields Considering Finite Strain Hyperelasticity

We propose a physics-informed machine learning framework called P-DivGNN to reconstruct local stress fields at the micro-scale, in the context of multi-scale simulation given a periodic micro-structure mesh and mean, macro-scale, stress values. This method is based in representing a periodic micro-structure as a graph, combined with a message passing graph neural network. We are able to retrieve local stress field distributions, providing average stress values produced by a mean field reduced order model (ROM) or Finite Element (FE) simulation at the macro-scale. The prediction of local stress fields are of utmost importance considering fracture analysis or the definition of local fatigue criteria. Our model incorporates physical constraints during training to constraint local stress field equilibrium state and employs a periodic graph representation to enforce periodic boundary conditions. The benefits of the proposed physics-informed GNN are evaluated considering linear and non linear hyperelastic responses applied to varying geometries. In the non-linear hyperelastic case, the proposed method achieves significant computational speed-ups compared to FE simulation, making it particularly attractive for large-scale applications.

Manuel Ricardo Guevara Garban, Yves Chemisky, Étienne Prulière +1

Univ. Bordeaux, CNRS, Bordeaux INP, I2M, UMR 5295, Talence 33400 France · Univ. Bordeaux, CNRS, Bordeaux INP, LaBRI, UMR 5800, Talence 33400 France · Arts et Metiers Institute of Technology, CNRS, Bordeaux INP, I2M, UMR 5295, Talence 33400 France

Physics-Informed GNNsStructural MechanicsHyperelasticity
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