The conversion between thermal snap-through and bifurcation instabilities of metal foam sandwich beams by refined first-order shear theory

An arch-shaped beam with different configurations under electrostatic loading experiences either the direct pull-in instability or the snap-through first and then the pull-in instability. When the pull-in instability occurs, the system collides with the electrode and adheres to it, which usually causes the system failure. When the snap-through instability occurs, the system experiences a discontinuous displacement to flip over without colliding with the electrode. The snap-through instability is an ideal actuation mechanism because of the following reasons: (1) after snap-through the system regains the stability and capability of withstanding further loading; (2) the system flips back when the loading is reduced, i.e. the system can be used repetitively; and (3) when approaching snap-through instability the system effective stiffness reduces toward zero, which leads to a fast flipping-over response. To differentiate these two types of instability responses for an arch-shaped beam is vital for the actuator design. For an arch-shaped beam under electrostatic loading, the nonlinear terms of the mid-plane stretching and the electrostatic loading make the analytical solution extremely difficult if not impossible and the related numerical solution is rather complex. Using the one mode expansion approximation and the truncation of the higher-order terms of the Taylor series, we present an analytical solution here. However, the one mode approximation and the truncation error of the Taylor series can cause serious error in the solution. Therefore, an error-compensating mechanism is also proposed. The analytical results are compared with both the experimental data and the numerical multi-mode analysis. The analytical method presented here offers a simple yet efficient solution approach by retaining good accuracy to analyze the instability of an arch-shaped beam under electrostatic loading.

Snap-through instability of helicoidal composite imperfect beams surrounded by nonlinear elastic foundation

Snap-through and bifurcation instability of FGM sandwich beams in thermo-mechanical loads by an extended analytical method

Aeroelastic characteristics of magneto-rheological fluid sandwich beams in supersonic airflow

Nonlinear instability analyses of channel-section beams subjected to minor-axis pure bending

This paper investigates the nonlinear response of doubly curved functionally graded material sandwich panels resting on elastic foundations, exposed to thermal environments and subjected to uniform external pressure. The material properties of both face sheets and core layer are assumed to be temperature dependent, and effective material properties of functionally graded material layers are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Formulations are based on first-order shear deformation shell theory taking geometrical nonlinearity, initial geometrical imperfection, Pasternak type elastic foundations, and tangential edge constraints into consideration. Approximate solutions are assumed to satisfy simply supported boundary conditions and Galerkin procedure is applied to derive expressions of buckling loads and nonlinear load–deflection relation. The effects of material, geometry and foundation parameters, face sheet thickness ratio, initial geometrical imperfection, thermal environments and degree of tangential restraint of edges on the snap-through instability, and nonlinear response of spherical and cylindrical functionally graded material sandwich panels are analyzed and discussed in detail.

Mode II dominant fracture of layered composite beams and wide-plates: a homogenized structural approach

Static indentation responses of foam sandwich beams and plates reinforced by fiber columns are investigated experimentally and theoretically. Based on the superposition principle, a new model is established for predicting the indentation response of sandwich beams. It should be pointed out that this model does not need to calculate the strain energy stored in the structure, which is usually difficult to be determined. For traditional foam sandwich beams and foam sandwich beams reinforced by fiber columns, the analytical predictions of indentation behaviors well agree with experimental measures. Furthermore, the analytical solution of indentation response of foam sandwich plate reinforced by fiber columns is derived by the principle of minimum energy and is compared well with experimental results.

This paper investigates the lateral-torsional instability of soft-core sandwich beams. This physical phenomenon, which has received limited attention in the framework of sandwich structures, is investigated here in the context of fully nonlinear analysis for the first time. The research addresses, quantifies, and explores the lateral-torsional instability with emphasis on the unique features of the sandwich structure and its geometrically nonlinear response. The research questions relate to the nature of the instability and to the role of the deformability of the core layer in the unique mechanism. The results of the investigation include a new, high-order, nonlinear model for the analysis of the torsional-lateral response as well as new insight into the evolution of the phenomenon in sandwich beams.

The effect of length and thickness on dynamic stability analysis of cantilever cylindrical shells under follower forces is addressed. Beck's, Leipholz's, and Hauger's problems were solved for cylindrical shells with different length-to-radius and thicknesses-to-radius ratios using the Galerkin method. First-order shear theory was used, and rotary inertias were considered in deriving the differential equations. Critical circumferential and longitudinal mode numbers and loads were evaluated for each case. Diagrams containing nondimensional load parameters vs. length and thickness parameters were plotted for each problem. For some shells with small length-to-radius ratios, flutter occurred in high longitudinal mode numbers where the first-order shear theory may not suffice to accurately evaluate the deformations. However, for long and moderately thick shells, there are ranges in which the shell can be analyzed using the simplified equivalent beam model.

Fabrication and mechanical testing of glass fiber entangled sandwich beams: A comparison with honeycomb and foam sandwich beams

This study aims to investigate the thermal buckling behaviour of thick homogeneous and functionally graded aluminiumbased beams using Reddy’s higher-order shear deformation theory. Recognising the limitations of classical and first-order theories in capturing shear effects and temperature-induced material degradation, a refined numerical model was developed to assess the stability of aluminium beams reinforced with Al2O3 and TiC under thermal loading. The material properties were assumed to vary through the beam thickness according to a power-law distribution, and temperature-dependent stiffness degradation is incorporated to mimic realistic high-temperature conditions. Three beam configurations, viz. a homogeneous aluminium beam, an Al-Al2O3 FG beam, and an Al-TiC functionally graded beam, were analysed over a temperature range of 30°C to 430°C and multiple gradation indices. The core novelty lies in the unified application of Reddy’s higher-order shear deformation theory combined with temperature-sensitive gradation to evaluate and compare the thermal buckling response across these three configurations. The results revealed a clear decline in critical buckling load with rising temperature across all cases. Functionally graded beams demonstrated superior buckling resistance compared to the homogeneous counterpart, with the Al-TiC configuration showing the highest critical buckling load values due to the high stiffness and thermal resilience of TiC. Among all gradation profiles, a lower power-law index (k = 1) emerged as optimal, offering up to 246% enhancement in critical buckling load. This work underscored the advantages of material gradation in enhancing thermal stability and validated the effectiveness of Reddy’s higher-order shear deformation theory in modelling thermomechanical instability in advanced composite beams. The insights gained can enhance the design of high-temperature structural components for aerospace, energy, and defence applications. Major Findings: The study proved that functionally graded beams reinforced with TiC demonstrated 246% more thermal buckling resistance than homogeneous aluminium beams. Optimal performance was observed at lower gradation indices (k = 1), where ceramic content near the compressive region enhanced stiffness. Reddy’s higher-order shear deformation theory proved effective in accurately capturing nonlinear shear effects and temperature-dependent material degradation.

Parametric instability of a dual-cored sandwich beam

Parametric instability of a sandwich beam under various boundary conditions

Nonlinear dynamic instability analysis of sandwich beams with integral viscoelastic core using different criteria