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Copyright of Engineering Mechanics / Gongcheng Lixue is the property of Engineering Mechanics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

AbstractPiezoelectric functionally graded porous plates reinforced by graphene platelets (PFGP-GPL) are frequently subjected to extreme thermal environments, large amplitude excitation and strong electric fields. It is a significant challenge to accurately predict the nonlinear frequency of PFGP-GPL under thermo-electro-mechanical loads. In this article, we propose a nonlinear isogeometric analysis model that comprehensively considers geometric nonlinearity, piezoelectric nonlinearity, and temperature dependence. Using the nonlinear constitutive equations and the Von Kármán nonlinear strain-displacement relationships, the nonlinear isogeometric equation for PFGP-GPL under thermo-electro-mechanical loads was established based on the Halpin–Tsai micromechanics model and first-order shear deformation theory. Subsequently, the nonlinear fundamental frequency of the PFGP-GPL under thermo-electro-mechanical loads is determined using an iterative method, and the accuracy of the model is validated through comparison with existing literature. Based on the nonlinear isogeometric formulation considering the effects of geometric nonlinearity, piezoelectric nonlinearity and temperature dependence, we conduct further studies on the effects of different GPL and porosity parameters, temperature, and voltage on the nonlinear frequency of the PFGP-GPL. The findings indicate that these factors exert a considerable influence on the nonlinear frequency of PFGP-GPL. [ABSTRACT FROM AUTHOR]

The special configuration and elongated geometrical appearance of the helical strand give it properties of tensile–torsion–bending coupling as well as macroscopic geometrical nonlinearity. Simulating small-scale strands using solid elements in finite element software reproduces these properties but is time-consuming. Current methods of modeling large-scale strands using cable elements or beam elements can account for geometric nonlinearities, but often fail to adequately consider the tensile–torsion–bending coupling characteristics of the strand cross-section. This study presents a new finite element method for modeling strand structures. This analysis method adopts the rigid body rule to handle the geometric nonlinearity of strand structures, considering the tensile–torsion–bending coupling characteristics of the strand cross-section, while remaining acceptable in terms of analysis time. The analytical method can provide the strand structure’s displacement and the parameters of the tension–torsion–bending coupling characteristics of the strand element. The results obtained from the proposed analytical method were compared with those from numerical modeling and experimental testing, confirming the validity of the analytical method. [ABSTRACT FROM AUTHOR]

We develop a new numerical-analytic method for solving geometrically nonlinear problems of bending of complex-shaped plates. The statement of the problem is realized within the framework of a refined higher-order theory, which takes into account the quadratic law of distribution of the transverse tangential stresses over the thickness. For linearization of the nonlinear problem, we apply the method of continuous extension with respect to the parameter. For the variational statement of the linearized problem, we construct a functional in the Lagrange form given on the kinematically admissible rates of displacements and the rates of shear functions. To find the main unknowns in the problem of nonlinear bending of a plate, we formulate the Cauchy problem for a system of ordinary differential equations. This Cauchy problem is solved by the Runge–Kutta–Merson method with automatic choice of the step. The right-hand sides of the differential equations (corresponding to the Runge–Kutta–Merson scheme) are found for fixed values of the parameter of loading from the solution of the variational problem for the Lagrange functional. The variational problems are solved by the Ritz method in combination with the R-function method. The test problems are solved for the cases of a rigidly restrained plate and a simply supported plate subjected to the action of uniformly distributed loads of different intensities. The problem of bending of plates of complex shape is solved. The influence of the geometric shape on the stress-strain state is investigated. [ABSTRACT FROM AUTHOR]

Intelligent magneto-responsive structures are widely used due to their fast response speed and noncontact control. In this study, the peeling behavior of a slender magneto-responsive sheet under the magnetic field's action is investigated experimentally and theoretically. Firstly, two identical magneto-responsive sheets, with the liquid film adhesion and the absence of the liquid film respectively, are analyzed under the control of a cylindrical magnet. In addition, the peeling process is abstracted via the classical elastica model, and the expression of the potential energy functional is established. The approximate solutions of the deflection and the adhesion length of the magneto-responsive sheets during the peeling process are obtained based on the Rayleigh–Ritz method. The effects of the magnetic field generated by cylindrical magnets and the work of adhesion on the maximum deflection and adhesion length of magneto-responsive sheets are further predicted. The theoretically approximate solution agrees very well with the experimental data. These findings can provide new implications in a wide range of industrial areas, such as medical microsensors and intelligent structures for drug delivery. [ABSTRACT FROM AUTHOR]

This paper deals with the analysis of wave propagation characteristics in various prestressed structures with geometric nonlinearities using the Carrera Unified Formulation (CUF). CUF provides a versatile platform to model a wide range of structures and nonlinearities that can take care of all wave propagation aspects. In this work, different geometric nonlinearities for which representative governing equations have been derived and numerical solutions have been obtained through a unified approach are considered. The study investigates in detail the effect of prestress and geometric nonlinearity on wave propagation behavior. The results indicate that prestress has a very influential effect on modal frequency and dispersion characteristics for wave propagation. Specifically, three CUF-modeled beams are considered herein, having a sandwich, metallic portal, and metallic box cross section, respectively. Initially, the principal cross-sectional modal shapes of the unstressed, linear, and full nonlinear (i.e., full three-dimensional Green-Lagrange strain matrix) beam with a prestress are investigated, among which torsional and flexural modes can be recognized. Afterward, the equilibrium curves of such structures for various geometrical nonlinear approximations are traced, highlighting that most types of nonlinearity induce a hardening behavior in the system, which increases with the preload, directly leading to a variation in modal frequencies. The dispersion relations of the full nonlinear structure examined as a function of the applied preload are further compared, enriching the investigation by exploiting wave finite element method capabilities. This knowledge paves the way toward the design and optimization of prestressed systems with enhanced acoustic performance, and that fosters the development of sound absorption, noise insulation, and structural isolation. [ABSTRACT FROM AUTHOR]

The actual capacity of a reinforced concrete (RC) structure is determined by the overstrength capacity of individual members. RC members can undergo six stages (namely cracking, yielding, spalling, buckling, crushing and rupturing) depending on the cross‐section geometry, reinforcement detailing, and type of loading. For members under compression and flexural actions, buckling of longitudinal bars becomes the ultimate stage in the load‐deformation curve of RC member. Hence, to assess the capacity of RC members, it is essential to have load‐deformation relation of individual bars considering nonlinear effects. This paper presents a simplified analytical procedure of nonlinear analysis to obtain the nonlinear load‐deformation curve of reinforcing bars. The proposed method uses combined geometric and material nonlinearity. The method is compared with the experimental test results from the literature and has shown a good match. Furthermore, the effect of initial imperfection and slenderness of the reinforcing bars on the overall performances have been studied and discussed. This inelastic relation of reinforcements has been used to obtain the P–M interaction diagram of the RC member, demonstrating the effect of nonlinearity in the longitudinal bars. Fiber modeling approach has been used to draw the P–M curve, considering confinement of concrete, bilinear stress–strain of steel under tension and nonlinear under compression. Implications of amount of longitudinal reinforcement, grade of steel, initial imperfection and section size on the P–M curve have been studied. Results show that the nonlinearity of the longitudinal bar can reduce the capacity of the member by 15%. The strength reduction is higher for higher percentage of reinforcements and slender bars. This indicates that the P–M interaction curve exists at three levels, and is discussed in detail in the paper. It is recommended that the effect of bar nonlinearity should be considered in the capacity assessment of RC members. [ABSTRACT FROM AUTHOR]

High-aspect-ratio aeroelastic wings are essential for energy efficient greener aircraft with improved aerodynamic efficiency and performance. In this work, a computational procedure based on a coupled computational fluid dynamics (CFD)–computational structural dynamics (CSD) technique is established to study the static aeroelastic behavior of a high-aspect-ratio wing at various flow velocities. Since these wings are structurally very flexible and experience large deformations, the present fluid structure interaction (FSI) approach couples a Navier–Stokes (N–S) based CFD solver with a finite element method (FEM) based structural solver incorporating geometric nonlinearity. Here, the N-S solver is based on the finite volume method (FVM) and the nonlinear FE structural solver is based on the Newton-Raphson method. The capability of the present FSI technique is demonstrated by comparing tip displacements and twist angles of the wing with the available experimental and numerical data in the literature. The effect of wing deformations on the pressure coefficients (Cp) of the linear and geometrically nonlinear wing models is also discussed. It shows that the linear model overpredicts Cp as compared to the geometrically nonlinear wing model. Further, a detailed comparison of span-wise horizontal displacement, vertical displacement, twist distributions as well as lift and side forces is shown between the linear and nonlinear structural models at various flow velocities. Numerical results show significant difference between the linear and nonlinear structural models at higher flow velocities. It indicates that the design of high-aspect-ratio wings must consider FSI approach to capture their nonlinear static aeroelastic behaviour accurately. [ABSTRACT FROM AUTHOR]

Copyright of Builder (1896-0642) is the property of PWB MEDIA Zdzieblowski sp.j. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Multi-stable systems, known for having complex nonlinear dynamics, have been shown in past studies to outperform their linear counterparts when designed for operation in vibration energy harvesters. This work investigates the dynamics and performance of a multi-stable electromagnetic energy harvesting device. The objectives are to enhance the levels of generated power and evaluate the useful bandwidths for the various modes of stability. Nonlinearity is introduced through a set of inclined springs and strongly influenced by the geometric parameters, as the shape of the potential energy curves can be adjusted by the selection of these properties. The effect of the geometric parameters' uncertainties on the potential energy as a result of imperfections in manufacturing and installation, and the performance of the proposed harvester, is examined. A nominal tri-stable configuration is considered, and the sensitivity of the system to input design uncertainties is explored. The system's response bifurcation diagrams and dynamical characteristics as well as the power output under up- and reverse-sweeping excitations are also reported. It is shown that the overall response and effectiveness of the nominal multi-stable harvester may drastically change in terms of resonance regions, periodicity of the motion, and levels of harvested power. A series of mono-stable and bi-stable harvesters arise due to the presence of geometrical uncertainties. [ABSTRACT FROM AUTHOR]

Although rotating blades are designed to operate away from structural frequencies, internal resonance can still occur at certain rotation speeds, significantly affecting the blades' stiffness. Therefore, a detailed investigation of the resonance mechanisms of rotating blades, especially those introduced by nonlinearities, is crucial for structural design and optimization. To address this, a dynamic model of a functionally graded graphene/titanium alloy composite trapezoid plate is established to investigate the nonlinear dynamics of a rotating blade with varying cross-sections. The ordinary differential equations of the plate are formulated based on the energy method and Lagrange equations. The occurrence of 1:3 internal resonance in the trapezoid plate is identified through the analysis of linear and nonlinear free vibrations. Subsequently, the steady-state responses of the rotating plate in the case of 1:3 internal resonance are numerically calculated and verified using the approximation solution of the multiple scales method. Parametric studies are conducted to investigate the effects of rotation speed, taper ratio, excitation amplitude, and excitation frequency on the amplitude–frequency and amplitude–force curves. [ABSTRACT FROM AUTHOR]

The objective of this research is to evaluate the dynamic structural response of tall buildings subjected to wind loads, taking into account the influence of geometric nonlinearity and aerodynamic damping. The project focuses on a steel-concrete composite structure with 48 floors and a height of 172.8 m, examining its response to wind non-deterministic dynamic actions. The building finite element model was developed based on the Finite Element Method (FEM), using the ANSYS computational program, and considering the soil-structure interaction effect, with the objective of obtaining a realistic representation of the dynamic behavior. The building dynamic response was obtained based on the displacement and acceleration values, determined with the consideration of a wind velocity range between 5 m/s (18 km/h) and 45 m/s (162 km/h). The findings of this study indicate that when the effect of geometric nonlinearity was incorporated into the analysis, the dynamic response of the investigated building exhibited notable discrepancies. The maximum differences observed in the horizontal translational displacements and accelerations were 30% and 45%, respectively. In contrast, the inclusion of aerodynamic damping had a negligible impact on the structural dynamic response, with maximum differences of 5% for displacements and 10% for accelerations. [ABSTRACT FROM AUTHOR]

Featured Application: The presented work can support the design of more efficient airplanes, ships, and other structures utilizing composite materials. This paper presents a numerical investigation of delaminated composite plates using a 3D degenerated plate element, with a focus on geometric nonlinearity. An 8-noded degenerated element is used to model the composite plate, ensuring higher accuracy and computational efficiency. Delamination is modeled using Heaviside step functions, providing a clear representation of discontinuities. The Green–Lagrangian formulation is employed to incorporate geometric nonlinearity and to evaluate its effects on the deflection behavior of delaminated plates under load. The developed model is validated against existing literature, demonstrating its reliability. Subsequently, a comprehensive parametric study is conducted to evaluate the influence of various factors including lamina sequences, boundary conditions, load intensities, and the size and location of the delamination (considered at the center of the laminate). A uniformly distributed pressure load is applied across the entire plate to simulate realistic loading conditions. Additionally, the effects of multiple delaminations through the thickness of the laminate are explored, with key observations on their impact reported. The findings provide valuable insights into the structural performance of delaminated composite plates under nonlinear conditions. [ABSTRACT FROM AUTHOR]

In response to the shortcomings of insufficient efficiency in calculating geometric nonlinear features and high environmental impact in the current construction, this study explores the control of nonlinear geometric structures based on an updated Lagrangian model function in the construction. In this method, the change in the geometric nonlinear stiffness is analyzed using generalized stiffness parameters and a displacement increment method, and the iteration step size and loading/unloading directions are adjusted in the iteration process to achieve the convergence of the solution. In the simulation experiment, the proposed method took 126 s to calculate the incremental iteration steps 700 times in a conventional environment, which is 28.8% more efficient than the cross-sectional method. In the simulated disaster environment, the model took 1,615 s to calculate the ultimate load of 84 contact elements, which is 43.1% more efficient than the section method and 62.6% more efficient than the discrete analysis method. Experimental results showed that the displacement judgment calculation efficiency of the method proposed in this study is higher than that of other models under different loading and unloading conditions and even in geological disaster states. This method had high environmental adaptability in solving nonlinear building structures and could improve the efficiency of solving general nonlinear building results.

Constitutive relations and a method for analyzing the behavior of fiberglass during longitudinal bending under the combined influence of force factors and an alkaline medium were proposed. Both natural and numerical experimental designs were outlined. A new approach to solving the problem of longitudinal bending of a fiberglass beam with initial failure was introduced, without involving geometrically nonlinear relations. This approach proved to be applicable when the resulting beam configuration is a flat curve. The results of numerical calculations were presented. In the first case, the beam with initial failure was studied using the new approach along with the finite element method (FEM). In the second case, for verification, the problem was solved in a geometrically nonlinear formulation. The results obtained showed a strong agreement.

With the widespread application of fiber-metal laminates in various aerospace fields and the inherent presence of both material and geometric nonlinearities in composites, the prediction of nonlinear vibration characteristics of these structures holds particular importance. This study, based on the Jones–Nelson–Hui and von Kármán theories, utilizes the energy method and the orthogonal polynomial method to solve the differential equations and iteratively obtain the nonlinear natural frequencies and responses. Additionally, the complex modulus method is employed to calculate the nonlinear modal damping ratios. Experimental validation demonstrates the effectiveness of the proposed model, with a frequency error of less than 3.7%, a response error of less than 15.4%, and a damping error of less than 11.5% when compared with experimental results. Finally, the influence of elastic modulus, thickness, and ply configuration on the nonlinear vibration characteristics of the structure is investigated. The discussion reveals that titanium reduces vibrations but should not be too thick, while fiber thickness can be appropriately increased. [ABSTRACT FROM AUTHOR]

The scotch yoke inerter (SYI) is a new geometrically nonlinear vibration isolator with a smaller maximum transmissibility than linear inerter systems. The influence of internal friction and the damping effect on the response of the SYI system for seismic isolation can be significant and needs to be studied. In this study, a small-scale SYI is designed and tested, and an accurate model of SYI is developed for describing its dynamic behavior. Then, the motion equation of the coupled structure-SYI system is established, and several dynamic analyses are studied, including the amplitude-frequency response, the critical excitation amplitude, the backbone curve, the peak response, the starting frequency, and the linearization design, and many fitting expressions for engineering applications are proposed. Finally, the vibration isolation performance of SYI is investigated when friction and damping effects are considered or not, using a single-degree-of-freedom system and a building structure as examples. For harmonic excitations, the maximum transmissibility of the SYI system is superior to that of the linear inerter system, and its advantage becomes more obvious as the excitation amplitude increases. Its seismic isolation effect is slightly better than that of a linear inerter for seismic excitations, where the SYI considering friction and damping effects is better. Practical Applications: A scotch yoke inerter is a geometrically nonlinear inerter that is simple to construct, easy to implement, and has the advantage of variable inertance. The variation of inertance is reflected in two aspects: first, its nominal inertance can be changed by adjusting the location of the pin; second, its dynamic inertance is related to its deformation, which can provide greater negative stiffness effects for larger external excitations. The precise and simplified output force model of the scotch yoke inerter is provided, which can be applied to the calculation and verification of the output force in the design of scotch yoke inerters. Fitting expressions for the critical excitation amplitude, starting frequency, and linearization design are proposed, which can provide a theoretical basis for the application of scotch yoke inerters in base-isolated structures. Compared with traditional linear inerters, scotch yoke inerters have a better isolation control effect, and this control effect can be further improved by making reasonable use of the internal friction and the damping in SYI. [ABSTRACT FROM AUTHOR]

Carbon nanotubes (CNTs) exhibit a unique buckling behavior due to their slender tubular geometry and thin-walled circular cross section. This study aims to analyze effect of nonlinear cross-sectional deformation on buckling of CNTs. To accomplish this, CNTs are modeled as beam structures, and the analysis is conducted using the Variational Asymptotic Method (VAM) and a geometrically exact beam theory, as well as nonlinear finite element analysis (FEA). The study considers various loading cases, including pure axial compression and combined loading scenarios, such as bending-axial compression and torsion-axial compression. The results of the study indicate that inclusion of cross-sectional deformation-induced nonlinearity reduces the critical buckling load of CNTs. The reduction is 2–5% for pure axial compression and 10–40% for combined loading cases. The results are validated against existing literature and commercial finite element software, ABAQUS®. Additionally, parametric studies with different slenderness and radius-to-thickness ratios were carried out to further understand the impact of these parameters on buckling of CNTs. Finally, the study presents 3D deformed shapes of CNTs during buckling by combining the results of the 1D analysis and the 2D cross section analysis. The findings show that nonlinearity associated with radius-to-thickness ratio has a significant impact on the cross-sectional ovalisation of CNTs and is critical in evaluating their buckling behavior. This aspect of nonlinearity is often overlooked in continuum modeling methods of CNTs, making this study an important contribution to the field. [ABSTRACT FROM AUTHOR]

A rapid nonlinear aeroelastic framework for the analysis of the highly flexible wing with distributed propellers is presented, validated and applied to investigate the propeller effects on the wing dynamic response and aeroelastic stability. In the framework, nonlinear beam elements based on the co-rotational method are applied for the large-deformation wing structure, and an efficient cylinder coordinate generation method is proposed for attached propellers at different position. By taking advantage of the relatively slow dynamics of the high-aspect-ratio wing, propeller wake is modeled as a quasi-steady skewed vortex cylinder with no updating process to reduce the high computational cost. Axial and tangential induced velocities are derived and included in the unsteady vortex lattice method. For the numerical cases explored, results indicate that large deformation causes thrust to produce wing negative torsion which limits the displacement oscillation, and slipstream mainly increases the response values. In addition, an improvement of flutter boundary is found with the increase of propeller thrust while slipstream brings a destabilising effect as a result of the increment of dynamic pressure and local lift. The great potential of distributed propellers in gust alleviation and flutter suppression of such aircraft is pointed out and the method as well as conclusions in this paper can provide further guidance. [ABSTRACT FROM AUTHOR]

Partially cable-stayed bridges have the characteristics of continuous rigid-frame bridges and cable-stayed bridges, making them a novel composite bridge system. This study focuses on the construction project of a multi-tower high-pier curved partially cable-stayed bridge to investigate the bridge's stability during construction. The Midas/Civil software was used to establish a model for key construction stages of the bridge, considering structural linear elasticity and geometric nonlinearity. The study examines the impact of static wind loads, asymmetric construction of the main girder, closure sequence, and the load and detachment of the hanging basket on the bridge's stability during construction. The results indicate that static wind loads have a significant impact on structural geometric nonlinearity, with a maximum reduction of 4.99%. Asymmetric construction at both ends of the main girder can cause structural instability and should be avoided. The geometric nonlinearity stability coefficient for the hanging basket load decreased by 10.83% during the maximum no-cable stage and by 7.84% during the cable stage, significantly affecting the stability during construction. A bridge closure sequence of side-span, secondary midspan, and midspan provides the most stable condition during the construction phase. The results of this study can inform the construction of similar partially cable-stayed bridges. [ABSTRACT FROM AUTHOR]

AbstractThis paper proposes a geometrically nonlinear wind-induced vibration piezoelectric energy harvester (WIVPEH) with a maximum size of only 80 mm. Introducing nonlinearity solely through geometric structure design reduces the overall stiffness of the system, enabling the device to excite multi-mode coupling and induce internal resonance even under low wind speed conditions, thereby broadening the bandwidth. Wind tunnel experiments demonstrated that the device could vibrate at a wind speed of 1.5 m/s. Under low wind speed, the piezoelectric output is about 4 times greater than that of ordinary devices. Our research indicates that the designed device can maintain efficient wind energy collection within a low wind speed range. [ABSTRACT FROM AUTHOR]

A rhombus-nested compliant amplification mechanism is proposed for versatile usages of precision actuators and force sensors with an easy tuning of stiffness. Such a monolithically planar rhombus-nested compliant mechanism has the dual functions of two-stage displacement or force amplification by changing the input and output ports. It features a large ratio of inter-stage stiffness, thus resulting in an enhanced amplification ratio, load capacity and dynamic bandwidth. The geometrically nonlinear analytical equations of displacement amplification ratio and input stiffness are derived in the presence of pronounced axially-loaded stiffening and kinematic-arching effects based on the beam constraint model. It allows an insightful evaluation of geometrically nonlinear deformation behaviors sensitive to structural dimensions in a parametric way. Insights into geometrically nonlinear behaviors in the case of large-stroke and axially-loaded motions are discussed as well. A proof-of-concept prototype with embedded piezoelectric stacks is fabricated with the dimensions of 74mm × 60mm × 10 mm. The dual functions of precision actuator with amplified motion strokes and force sensor with enhanced sensitivity are experimentally demonstrated. [Display omitted] • A monolithically rhombus-nested compliant amplification mechanism is designed. • Geometrically nonlinear analytical model of amplification ratio is derived. • The dual functions of a precision actuator and force sensor are demonstrated. [ABSTRACT FROM AUTHOR]

An extremely simplified transformation model of dynamic deformatio of a strip consisting of two sections along its length is constructed. It is based on the classical geometrically nonlinear Kirchhoff–Love rod model on the loose section, and the fixed section of finite length is considered to be attached to the rigid and fixed support element via elastic layers. On the fixed section, the deflections of the rod and interlayers are considered zero, and for displacements in the axial direction over the thicknesses of the rod and interlayers, approximations are adopted according to the Timoshenko shear model subject to the continuity conditions at the points of their junction with each other and immobility at the points of attachment of the interlayers to the support element. The conditions for the kinematic coupling of the unfixed and fixed sections of the rod are formulated, and, based on them, using the d'Alembert–Lagrange variational princinple, the corresponding equations of motion and boundary conditions, as well as the static conditions for coupling the sections, are derived for the sections under consideration. [ABSTRACT FROM AUTHOR]

The geometrically nonlinear problem for a long rectangular sandwich plate under a uniform surface load has been formulated and analytically solved. The basic equations have been derived using the geometrically nonlinear theory in the quadratic approximation, the curved-normal hypothesis, and Hooke's law for transversely isotropic materials. The exact expressions for the components of the stress-strain state of the sandwich plate with clamped longitudinal edges have been obtained. Numerical results for both the geometrically nonlinear and the linear boundary value problems have been presented for three options of mechanical parameters of the core material. [ABSTRACT FROM AUTHOR]

This paper reviews the recent advances on the combination of component mode synthesis and model order reduction for geometrically nonlinear analysis, focusing on fixed-interface substructures and non-intrusive reduced-order models. These approaches offer significant potential for engineering applications by enabling accurate mechanical behavior prediction without detailed geometric and material information. Additionally, they facilitate safe sharing and collaboration between companies, reducing design times and production costs while also offering computational efficiency. However, challenges remain, indicating the need for future improvements in this area. [ABSTRACT FROM AUTHOR]

Bending active structures involve the deformation of originally flat structures during the erection process. These structures offer a promising approach to enhance design sustainability. However, despite advancements in structural computational methods, their implementation is still limited. This paper examines the constraints associated with this design approach from a designer's perspective and proposes potential solutions. From this analysis, a design method is developed that utilizes additive manufacturing to explore different solutions during the concept stage. Prior to the form-finding process, a flat, variable-density pattern is created within a parametric environment. This pattern, referred to as the "Soft Pattern based on Control Points" (SPSCP), incorporates multiple design variables to accommodate diverse design requirements. In this preliminary study, we compare the impact of varying the design parameters on a small-scale model, as observed by the naked eye, and through finite element analysis. [ABSTRACT FROM AUTHOR]