Abstract Multistable laminates are potential candidates for adaptive structures due to the existence of multiple stable states. Commonly, such bistable shapes are generated from the cool-down process of the unsymmetric laminates from the curing temperature. In this work, we exploit unsymmetric variable stiffness laminates with curvilinear fiber paths to generate similar bistable shapes as unsymmetric cross-ply laminates, but with the possibility to tailor the snap-through loads. Snap-through is a complex phenomenon in that is difficult to characterize using simple analytical models. An accurate yet computationally efficient semi-analytical model is proposed to compute the snap-through forces of bistable variable stiffness (VS) laminates. The differential equations resulting from the compatibility and the in-plane equilibrium equations are solved with negligible numerical error using the Differential Quadrature Method (DQM). As a result, the in-plane stress resultants and the total potential energy is written in terms of curvatures. The out-of-plane displacements are expressed in the form of Legendre polynomials where the unknown coefficients of the displacement function are found using the Rayleigh-Ritz formulation. The calculated snap-through loads are then compared with the Finite Element (FE) results. A parametric study is conducted to explore the tailoring capabilities of VS laminates for snap-through loads.

中文翻译：

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一种有效的半解析框架，用于在双稳态可变刚度层压板中定制快速通过载荷

摘要 由于存在多个稳定状态，多稳态层压板是自适应结构的潜在候选者。通常，这种双稳态形状是由不对称层压板在固化温度下的冷却过程产生的。在这项工作中，我们利用具有曲线纤维路径的非对称可变刚度层压板来生成与非对称交叉层层压板类似的双稳态形状，但可以定制快速通过载荷。快速通过是一种复杂的现象，因为它很难用简单的分析模型来表征。提出了一种准确但计算效率高的半解析模型来计算双稳态可变刚度 (VS) 层压板的快速通过力。使用微分正交法 (DQM) 求解由兼容性和平面内平衡方程产生的微分方程，数值误差可忽略不计。结果，面内应力合力和总势能以曲率表示。平面外位移以勒让德多项式的形式表示，其中位移函数的未知系数是使用瑞利-里兹公式找到的。然后将计算出的快速载荷与有限元 (FE) 结果进行比较。进行了一项参数研究，以探索 VS 层压板的剪裁能力，以应对快速通过载荷。面内应力合力和总势能以曲率表示。平面外位移以勒让德多项式的形式表示，其中位移函数的未知系数是使用瑞利-里兹公式找到的。然后将计算出的快速载荷与有限元 (FE) 结果进行比较。进行了一项参数研究，以探索 VS 层压板的剪裁能力，以应对快速通过载荷。面内应力合力和总势能以曲率表示。平面外位移以勒让德多项式的形式表示，其中位移函数的未知系数是使用瑞利-里兹公式找到的。然后将计算出的快速载荷与有限元 (FE) 结果进行比较。进行了一项参数研究，以探索 VS 层压板的剪裁能力，以应对快速通过载荷。