Abstract A corotational finite-element formulation is developed for piezoelectric plane frames subject to small strains but large deformations. In the corotating (local) system, the element is linear and superconvergent, with no electrical degrees of freedom. The formulation is derived from a piezoelectric beam theory that incorporates the Timoshenko displacement assumption and assumes a quadratic variation of the electric potential through the thickness of each piezoelectric patch. All linearizations required by the Newton–Raphson solution procedure, including those related to certain induced follower loadings, are explicitly and consistently derived. The proposed formulation (a) avoids membrane, transverse shear, and piezoelectric lockings; (b) yields assembled stiffness matrices that are not affected by the high condition numbers, typically found in piezoelectric finite-element models; (c) requires no special corotational algorithm; and (d) effectively handles large deformations, as demonstrated through numerical examples, including shape control applications.
Abstract Exposure to high temperatures severely deteriorates concrete mechanical performance and aggravates the intrinsic stochasticity of its deformation response, creating critical obstacles to the reliability evaluation of fire-damaged concrete structures. Distinct from concrete at ambient temperature, specimens heated to elevated temperatures display prominent stress–strain dispersion from the very start of uniaxial compression, and this scatter becomes more significant with rising temperatures. Traditional stochastic damage models that merely treat fracture strain as a random variable cannot reproduce this early-stage random fluctuation accurately. Within the mesoscopic stochastic fracture framework, this paper develops a novel constitutive model by introducing two statistically independent random fields for elastic modulus and fracture strain, and derives closed-form analytical formulas for the mean and variance of full-range stress–strain curves. The model is fully calibrated and verified against systematic uniaxial compression test data covering four concrete strength grades and multiple thermal levels with abundant replicate specimens. Validation outcomes revealed that high temperatures generate additional elastic-stage randomness driven by spatially uneven thermally induced microstructural deterioration. The scattered ascending segment of stress–strain curves is governed by the randomness of elastic modulus, whereas peak bearing capacity and postpeak softening evolution are controlled by the variability of fracture strain. Comparative analyses demonstrated that the dual-random-field model outperforms classic single-random-field formulations in capturing both average mechanical behavior and probabilistic dispersion, particularly for the ascending branch under medium and high temperatures. The established model delivers a solid constitutive foundation for probabilistic analysis and fire safety assessment of concrete structures under thermal exposure.
Abstract This study develops an improved self-weight consolidation model with a power law time-dependent function to characterize the bleeding process in fresh concrete paste. The model is verified by two experimental datasets with varying mix proportions and water–cement ratios. It is superior in fitting accuracy and more effective characterization of the bleeding process compared to the conventional self-weight consolidation model. Derivative analysis of the bleeding curves reveals that the model accurately captures the initial acceleration followed by gradual deceleration of bleeding rates. The time-scale transformed power law function effectively establishes the relationship between the mesoscopic time–space fabric of fresh concrete paste and the time-dependent characteristics of the bleeding process. Notably, the three fitted parameters of the proposed model exhibit distinct quantitative relationships with water–cement ratio variations.
The eigenfunction superposition method is established for unsteady porous medium flow in long ducts of arbitrary cross section. The method utilizes the eigenfunctions of the Helmholtz equation to solve the Darcy-Brinkman equation. The method is much simpler than traditional separation of variables or Laplace transform, and the result can be expressed in simple summations. The unsteady flow in an isosceles right triangular duct, studied for the first time, is presented as an illustration.
Load path analysis serves as the foundation for establishing mechanical models of D-regions in structural components. This paper proposes a method based on Fermat's principle for the automatic generation of load paths within structural members. First, based on the governing equations of elastodynamics and utilizing the Wentzel-Kramers-Brillouin-Jeffreys high-frequency asymptotic expansion, we demonstrate a geometric analogy between the ray paths of high-frequency body waves in inhomogeneous media and load flow transmission paths. Subsequently, by constructing a virtual refractive index field applicable to material inhomogeneity and damage degradation, we transform the determination of load paths into an optimal routing problem subject to boundary, obstacle, and topological constraints and introduce a numerical solution employing Bezier curve parameterization coupled with a hybrid Monte Carlo and hill-climbing algorithm. Finally, analyses of several classical cases indicate that the proposed method can automatically generate load paths characterized by both physical autonomy and geometric smoothness, demonstrating high accuracy and broad applicability.
