Rongqiao Xu

Accurate modeling of the contact between a mold and an imprint resist under finite deformation remains a critical challenge in nanoimprint lithography. This paper presents a theoretical framework for analyzing thermoelastic contact problems in pre-deformed hyperelastic materials. Within the framework of nonlinear thermoelasticity, incremental governing equations are derived in the updated Lagrangian formulation. General solutions to the incremental governing equations are expressed as combinations of quasi-harmonic functions based on the generalized Almansi’s theorem. The potential theory method is developed to solve the problem of frictionless thermoelastic contact between a rigid indenter and a hyperelastic half-space under prescribed incremental mechanical and thermal boundary conditions. Single-layer potentials are constructed, and their densities are explicitly obtained by inverting the resulting integro-differential equations. Closed-form expressions obtained for incremental displacement, temperature field, stress components, and incremental indentation force are validated through finite element simulations, showing excellent agreement for small perturbations. This framework is then extended to a hyperelastic film bonded to a rigid substrate using the generalized image method, where Fredholm integral equations of the second kind arise and are solved iteratively by establishing contraction mappings according to the Banach-Caccioppoli theorem. For wavy surfaces, adhesive contact is analyzed using an energy release rate criterion, leading to an extended JKR model that incorporates thermal effects, pre-stretch, and surface topography. The modified JKR solution reveals that pre-stretch can modulate waviness amplitude and wavelength, thereby enabling tunable interface strength. Surface instability-induced waviness is further investigated, where a computational buckling analysis in the total Lagrangian formulation is performed to generate initial imperfections, followed by contact simulation using the augmented Lagrangian method. This work establishes a systematic analytical foundation for thermoelastic contact in soft materials under finite deformation, with implications for precision surface engineering and manufacturing.

Accurate modeling of the contact between a mold and an imprint resist under finite deformation remains a critical challenge in nanoimprint lithography. This paper presents a theoretical framework for analyzing thermoelastic contact problems in pre-deformed hyperelastic materials. Within the framework of nonlinear thermoelasticity, incremental governing equations are derived in the updated Lagrangian formulation. General solutions to the incremental governing equations are expressed as combinations of quasi-harmonic functions based on the generalized Almansi's theorem. The potential theory method is developed to solve the problem of frictionless thermoelastic contact between a rigid indenter and a hyperelastic half-space under prescribed incremental mechanical and thermal boundary conditions. Single-layer potentials are constructed, and their densities are explicitly obtained by inverting the resulting integro-differential equations. Closed-form expressions obtained for incremental displacement, temperature field, stress components, and incremental indentation force are validated through finite element simulations, showing excellent agreement for small perturbations. This framework is then extended to a hyperelastic film bonded to a rigid substrate using the generalized image method, where Fredholm integral equations of the second kind arise and are solved iteratively by establishing contraction mappings according to the Banach-Caccioppoli theorem. For wavy surfaces, adhesive contact is analyzed using an energy release rate criterion, leading to an extended JKR model that incorporates thermal effects, pre-stretch, and surface topography. The modified JKR solution reveals that pre-stretch can modulate waviness amplitude and wavelength, thereby enabling tunable interface strength. Surface instability-induced waviness is further investigated, where a computational buckling analysis in the total Lagrangian formulation is performed to generate initial imperfections, followed by contact simulation using the augmented Lagrangian method. This work establishes a systematic analytical foundation for thermoelastic contact in soft materials under finite deformation, with implications for precision surface engineering and manufacturing.

While both multi-axle trucks and composite girder bridges with corrugated steel webs (CSWs) have been widely implemented in the transport industry, there is limited analysis on the dynamic interaction between them. Composite girder bridges with CSWs generally exhibit complex dynamic behaviors that deviate from the Euler–Bernoulli beam theory. Based on prior static studies outlined using zig-zag theory, we present an efficient analytical method for the dynamic analysis of composite girder bridges with CSWs under multi-axle truck loading scenarios. The developed framework addresses the challenges associated with the dynamic analysis of both continuous and tapered composite girder bridges subjected to different multi-axle trucks, providing both computational efficiency and analytical flexibility. Composite girder bridges with CSWs are modeled as a sandwich beam under conditions of extreme inter-layer modulus mismatch. The accuracy of the analytical method for dynamic analysis is validated through finite element method (FEM). The dynamic amplification factors (DAFs) for both shear force and bending moment of tapered girder bridges with CSWs are systematically investigated through designed numerical examples. By introducing a series of standard composite girder bridges with different cross-sections, span lengths, road surface conditions, girder types and truck loading scenarios, a parametric analysis is conducted to examine the amplified effects of the truck types, moving speed, the road surface condition, girder types and Resal effect on the dynamic response of girders with CSWs. The results highlight the limitations of current bridge design codes in determining DAFs for composite girders with CSWs and provide valuable insights for the design and optimization of such bridges.

Exposed to the vibrational energy induced by shield tunnelling construction, the tunnel lining faces potential risk while the vibration response of the lining is transmitted to adjacent areas. Using the state space method, a theoretical model for the longitudinal dynamic response of the lining is established, with which the natural frequencies and corresponding modal shapes of the lining are obtained. In the proposed model, the lining is simplified as uniform cross-sectional bars connected by a series of springs, by which the bolts between segment rings are simulated. The jack is represented by a concentrated spring. The lining-strata interaction is described by distributed springs. Subsequently, a shell-spring finite element model is established to verify the accuracy of the method. Furthermore, a parametric analysis is presented to reveal the influences of the coefficient of horizontal subgrade reaction in the strata, the spring stiffness of the bolts between the segment rings and the boundary condition at the launching working shaft on the longitudinal vibration characteristics of the lining. The results demonstrate that the frequencies of the lining are significantly influenced by the first two parameters. When the tunnel passes through heterogeneous strata, the amplitude of the modal shape of the lining in the soft strata is much greater than that in the hard strata. For the tunnel longer than 50 m, the frequencies of the lining differ by only 1.5% between fixed-end and free-end boundary conditions at the launching working shaft. The study provides an analytical approach to predict the dynamic response of the tunnel lining.

Fracture and instability may occur separately or concurrently, severely impairing the reliability of flexible electroactive devices. Based on the nonlinear theory of electroelasticity and incremental field theory, this work establishes general solutions to the governing equations for a soft electroelastic body subjected to particular yet common biasing fields. We use potential theory method to obtain and validate explicit analytical solutions of the resulting integrodifferential equations for both crack and anti-crack problems under various elementary loading conditions. We examine two types of surface instabilities in pre-deformed cracked electroactive bodies for perturbations in the x-z and ρ-z planes. To quantitatively describe the fracture and stability behavior, we further introduce incremental intensity factors and incremental energy release rates to assess crack propagation, together with a buckling topological number to classify crack-face buckling and persistent stability. The derived bifurcation equations further reveal re-entrant phenomena as pre-stretch and initial electrical displacement vary. Overall, the proposed framework provides unified, quantitative analysis for electromechanically coupled fracture and instability in soft electroelastic materials.

The longitudinal differential settlement (LDS) of bridge–subgrade transition section is a prevalent concern for bridges in coastal areas, since it acts as an additional source of excitation for vehicles when they enter the bridge. This study presents a numerical model that incorporates the effects of LDS into vehicle–bridge interaction (VBI) analysis, implemented a self-developed simulation program with enhanced computational efficiency that avoids interactive data transfer among multiple commercial software packages. Field tests are conducted for model validation, followed by numerical simulations for parametric analysis. The combined effects of LDS and other key parameters on VBI dynamics are systematically investigated with reference to prevailing design code, an influence that has been largely overlooked in design practice and previous research despite its potential impact on bridge dynamic performance. The effects of LDS on the performance of representative VBI-based technologies, including bridge weight-in-motion (BWIM) and vehicle scanning methods (VSM), are then examined. The results show that LDS increases both axle-load and gross-vehicle-weight identification errors in BWIM, while long-span bridges exhibit little sensitivity to LDS, particularly in wheelbase identification. Notably, despite increased complexity in the spectral components of VSM signals, the identification accuracy of VSM under severe impact conditions is improved.

To address the inherent inaccuracies of the classical beam theory (which overestimates the flexural stiffness) and the “quasi-plane section method” (which neglects the shear deformation) in the deflection analysis of steel truss web–concrete composite beams, this study homogenizes discrete steel truss web members into a continuous steel web with equivalent thickness based on the strain energy equivalence principle. This homogenization is conducted under the assumption of fixed-end constraints for web members, thus establishing a sandwich laminated beam model. Incorporating the assumptions of zigzag axial displacement and layer-wise quadratic parabolic transverse shear stress, this study adopts the governing equations for static bending of composite beams derived via Hamilton’s mixed energy variational principle—this theory eliminates the need for an artificial shear correction factor, as the transverse shear stress naturally satisfies the zero boundary conditions at the upper and lower surfaces and the continuity condition at the interlayers. Analytical solutions for bending deflection under uniformly distributed loads are derived and validated against three-dimensional (3D) finite element (FE) models. The analysis results of a 45-meter-span beam demonstrate that the relative error in the maximum deflection of both simply supported beams and cantilever beams calculated by the proposed method is approximately 5%, which is significantly superior to the classical beam theory; the deflection induced by the zigzag effect at the mid-span of simply supported beams accounts for 15% of the total deflection, making it an indispensable key component in structural design. This method enables accurate deflection prediction and provides reliable technical guidance for the preliminary design of steel truss web–concrete composite beam bridges.