Optimal Stiffness Research Articles

Sloshing reduction with passive spring–mass baffles in partially filled containers

The potential for sloshing reduction of passive, moving baffles with translational motion constrained by springs is investigated numerically in partially filled containers. Simulations are based on the level-set formulation, considering water as the liquid under study and a baffle made of aluminum; this selection allows for direct validation of the model against experimental and analytical data. Depending on the filling ratio V∈(0,1), which simply measures the volume of liquid relative to the total container size, one can find an optimal spring stiffness K(V) that minimizes the kinetic energy and decay time of the sloshing response when subjected to a pulse-like acceleration. Results show that moving baffles significantly reduce sloshing compared to their fixed counterparts, with decreases up to 84.6% in decay time, τd. Frequency analyses for different V reveal one or two resonances in the range of 0.1–1.5Hz whose amplitudes are directly influenced (lowered) by K, analogous to the behavior of Tuned Mass Dampers. For potential applications, the selection of K should look for an adequate sloshing response over the entire range of V, and account for both quasi-static and harmonic excitation, conveniently weighted in accord with the expected operational loads.

Seismic vulnerability analysis of palace-style timber structures base on lumped mass model considering column rocking effect

To investigate the influence of joint reinforcement on the vulnerability of palace-style ancient timber structures, a spring-rigid rod analysis model was established, considering the mechanical behavior of tenon-mortise joints, column base joints, and bracket set joints. A lumped mass model was proposed using the centroid method and stiffness equivalent method and the accuracy of the simplified model is verified through shake table tests. Additionally, the influence of reinforcement on tenon-mortise joints and bracket set joint on the seismic displacement response was investigated, the optimal reinforcement range for joints was determined. Finally, incremental dynamic analysis was conducted on the model considering joint reinforcement, and the influence of optimal joint reinforcement on the seismic vulnerability of timber structures was researched. The study found that the optimal stiffness enhancement of column frame mortise-tenon joints range from 4 to 6 times and the stiffness of bracket set joints by 2.9 times. The probability of structural collapse of reinforced both mortise-tenon joints and bracket set joints was reduced by 15.56 %. However, individually reinforcing either tenon-mortise joints or bracket set joints only slightly decreases the probability of collapse.

Performance Evaluation and Comparative Analyses of Tuned Inerter Damper for Stochastic Base Excited Structures Based on Hybrid H2/H∞ Optimization

Compared with tuned mass damper, tuned inerter damper (TID) has higher damping efficiency and lightweight characteristic if appropriate optimal methods are selected. Generally, [Formula: see text] or [Formula: see text] optimal methods are adopted to determine the optimal parameters of TID individually. But the vibration mitigation performance of the TID under near resonance frequency band based on [Formula: see text] optimization is less than [Formula: see text] optimization, but the peak frequency response based on [Formula: see text] optimization will be greater than [Formula: see text] optimization at the same time. Dual-characteristic-based vibration control may not be achievable based on [Formula: see text] or [Formula: see text] criteria, respectively. For this reason, hybrid [Formula: see text] optimization can be adopted. In this work, closed-form expressions are derived for the control of structural displacement responses based on hybrid [Formula: see text] optimal method. The vibration mitigation performance of the different optimized TIDs is evaluated considering the single-degree-of-freedom and multi-degrees-of-freedom systems are subjected to typical ground motions excitation. Results illustrate that because of the use of the optimal stiffness ratio of [Formula: see text] optimization and very close value of [Formula: see text] optimizations’ nominal damping ratio in [Formula: see text] optimization, [Formula: see text] optimization shows ‘dual characteristics’ in different excitation situations. Specifically, the peak response and structural fundamental frequencies’ response in displacement frequency response function using hybrid [Formula: see text] optimal methods are between [Formula: see text] and [Formula: see text] optimization, which indicates an excellent and balanced control performance combining the advantages of [Formula: see text] and [Formula: see text] optimal solutions. Hence, this hybrid method is more suitable for more complex ground motions excitation to control critical structural responses instead of single characteristic excitation. And the comprehensive vibration control in dynamic time histories analyses can be achieved by this dual characteristic-based optimal strategy. When designing the specific TID, hybrid [Formula: see text] optimization can be considered as the best choice for its compatibility and high adaptability for complex practical engineering scenarios with random and diverse excitations.

The influence of longitudinal bending stiffness on running economy and biomechanics in male and female runners

The purpose of this study was to evaluate the influence of different longitudinal bending stiffnesses (LBS) on running economy and lower extremity joint biomechanics in male and female runners. Thirty participants (15 F;15M) performed a treadmill protocol of five-minute randomised aerobic runs with four different footwear conditions varying in LBS: 16.1 N/mm; 32.7 N/mm; 46.1 N/mm; 90.1 N/mm. Biomechanical data was collected at the metatarsophalangeal (MTP) and ankle joints. Running economy was quantified via oxygen consumption data. Oxygen consumption observed no significant differences between footwear conditions (p = 0.960) or significant interaction between footwear and sex (p = 0.126). Stance time observed a significant difference between footwear conditions (p < 0.001), and a significant interaction of footwear and sex (p = 0.008), increasing in females as stiffness increased. At the MTP joint, a shoe effect was present for peak bending angle (p < 0.001), peak extension (p = 0.040) and flexion (p < 0.001) angular velocity, and energy generated at the joint (p = 0.010). There was also an interaction effect of peak MTP extension angular velocity (p = 0.044), with females slightly decreasing as stiffness increased, with no reaction from males. At the ankle joint, a shoe effect was present for peak dorsiflexion (p < 0.001) and plantarflexion (p < 0.001) angular velocity, peak negative power (p < 0.001) and energy absorbed at the joint (p < 0.001). Comparing the interaction between shoe condition and male/female runners, male and female runners reacted similarly to the increased LBS with no effect on running economy and subtle changes in the stance time and MTP angular velocity for female runners. While further research is needed in this area investigating aspects related to sex-specific optimal stiffness element location and geometry, it does not appear that the stiffness magnitude has a sex dependence.

Compound nested lattices with programmable isotropy and elastic stiffness up to the theoretical limit

A novel class of compound structures, which consists of 2 types of unit cell geometries occupying different sites in the lattice (i.e. compound lattice) was investigated. The arrangement and volume ratio of the 2 unit cell geometries were varied, and it was found that the compound lattices can exhibit up to 4 distinct geometries – 2 from the unit cells and 2 supra-structures from the arrangement of each type of unit cell. In stiffness optimization, the material re-organization tends to emphasize the stiffest of the 4 geometries and collapse the hierarchical compound lattice into a single-level structure. In isotropy optimization, unit cells had to be arranged into supra-structures with an anisotropy profile opposite to that of their geometries. These insights led to the introduction of the compound nested lattices, which exhibited higher specific moduli than previous isotropic designs. The compound nested 1pSC:512pFCC lattice, in particular, reached 97.9 % of the Hashin-Shtrikman upper bound at relative density = 0.6, which is the closest approach to the theoretical maximum ever reported.

Topology optimization of finite strain elastoplastic materials using continuous adjoint method: Formulation, implementation, and applications

This study presents a unified formulation of topology optimization for finite strain elastoplastic materials. As the primal problem to describe the elastoplastic behavior, we consider the standard J2-plasticity model incorporated into Neo-Hookean elasticity within the finite strain framework. For the optimization problem, the objective function is set to accommodate both single and multiple objectives, the latter of which is realized by weighting each sub-function. The continuous adjoint method is employed to derive the sensitivity, which is a general form that accepts any kind of discretization method. Then, the governing equations of the adjoint problem are derived as a format that holds at any moment and at any location in the continuum body or on its boundary. Accordingly, the proposed formulation is independent of any requirements in numerical implementation. In addition, the reaction–diffusion equation is used to update the design variable in an optimizing process, for which the continuous distribution of the design variable as well as material properties are maintained. Two specific optimization problems, stiffness maximization and plastic hardening maximization, for two and three-dimensional structures are presented to demonstrate the ability of the proposed formulation.

Ultra-stiff and quasi-elastic-isotropic triply periodic minimal surface structures designed by deep learning

Multi-functional triply periodic minimal surface (TPMS) structures have been widely studied and proven to have significant importance. Most studies are based on several typical TPMSs. However, some research suggests that the hybrid forms of the TPMSs can exhibit superior mechanical properties. The challenge lies in the unpredictability of the hybrid TPMS property. In this study, an approach is proposed for precisely identify the hybrid TPMS using fully connected neural network (FCNN) and particle swarm optimization (PSO) algorithm. A design space of four TPMSs hybridization is introduced and used to generate over 8000 samples. Stiffness constants obtained using the homogenization method is used in elastic characterization. The hybrid TPMSs is proved to lack common cubic symmetry but possess wide rotational symmetry. Indirect stiffness constant-based way exhibits better predictions for optimal stiffness and elastic isotropy than direct property parameter-based one. The approach successfully identified useful structures: quasi-elastic-isotropic ones and a ultra-stiff one that is ∼ 9 % stronger than the currently strongest TPMS. The method offers comprehensive guidance for stiffness constant-based TPMS design using DL technique.

A Novel Variable‐Stiffness Tail Based on Layer‐Jamming for Robotic Fish

Fish have excellent swimming performance, and one key factor is their ability to autonomously adjust body stiffness, which can help them efficiently swim at different speeds and complex environments. At present, the variable‐stiffness design of robotic fish still suffers from structural complexity, severe deformation, and small variation range, which limits the application of variable‐stiffness theory in robotic fish. In this article, a variable‐stiffness tail is designed based on layer‐jamming for robotic fish, which can conveniently achieve online stiffness adjustment while maintaining the optimal stiffness distribution and the shape is unaffected. A modeling method for the tail is proposed by combining the mechanical characteristics of the layer‐jamming structure with the pseudo‐rigid body model. To validate the performance of the tail, a series of experiments are conducted, which show that the stiffness variation range of the tail is around 10 times, and the accuracy of the model in predicting the kinematics of the tail is also verified. Moreover, the thrust tests demonstrate that stiffness adjustment is beneficial for fish swimming at different frequencies. The proposed variable‐stiffness tail will promote the development of efficient underwater biomimetic robots.

Biomechanical Investigation of Lower Limbs during Slope Transformation Running with Different Longitudinal Bending Stiffness Shoes.

During city running or marathon races, shifts in level ground and up-and-down slopes are regularly encountered, resulting in changes in lower limb biomechanics. The longitudinal bending stiffness of the running shoe affects the running performance. This research aimed to investigate the biomechanical changes in the lower limbs when transitioning from level ground to an uphill slope under different longitudinal bending stiffness (LBS) levels in running shoes. Fifteen male amateur runners were recruited and tested while wearing three different LBS running shoes. The participants were asked to pass the force platform with their right foot at a speed of 3.3 m/s ± 0.2. Kinematics data and GRFs were collected synchronously. Each participant completed and recorded ten successful experiments per pair of shoes. The range of motion in the sagittal of the knee joint was reduced with the increase in the longitudinal bending stiffness. Positive work was increased in the sagittal plane of the ankle joint and reduced in the keen joint. The negative work of the knee joint increased in the sagittal plane. The positive work of the metatarsophalangeal joint in the sagittal plane increased. Transitioning from running on a level surface to running uphill, while wearing running shoes with high LBS, could lead to improved efficiency in lower limb function. However, the higher LBS of running shoes increases the energy absorption of the knee joint, potentially increasing the risk of knee injuries. Thus, amateurs should choose running shoes with optimal stiffness when running.

A novel stiffness optimization model of space telescopic boom based on locking mechanism

A novel stiffness optimization model of space telescopic boom based on locking mechanism

Computational analysis of cancer cell adhesion in curved vessels affected by wall shear stress for prediction of metastatic spreading.

Introduction: The dynamics of circulating tumor cells (CTCs) within blood vessels play a pivotal role in predicting metastatic spreading of cancer within the body. However, the limited understanding and method to quantitatively investigate the influence of vascular architecture on CTC dynamics hinders our ability to predict metastatic process effectively. To address this limitation, the present study was conducted to investigate the influence of blood vessel tortuosity on the behaviour of CTCs, focusing specifically on establishing methods and examining the role of shear stress in CTC-vessel wall interactions and its subsequent impact on metastasis. Methods: We computationally simulated CTC behaviour under various shear stress conditions induced by vessel tortuosity. Our computational model, based on the lattice Boltzmann method (LBM) and a coarse-grained spectrin-link membrane model, efficiently simulates blood plasma dynamics and CTC deformability. The model incorporates fluid-structure interactions and receptor-ligand interactions crucial for CTC adhesion using the immersed boundary method (IBM). Results: Our findings reveal that uniform shear stress in straight vessels leads to predictable CTC-vessel interactions, whereas in curved vessels, asymmetrical flow patterns and altered shear stress create distinct adhesion dynamics, potentially influencing CTC extravasation. Quantitative analysis shows a 25% decrease in the wall shear stress in low-shear regions and a 58.5% increase in the high-shear region. We observed high-shear regions in curved vessels to be potential sites for increased CTC adhesion and extravasation, facilitated by elevated endothelial expression of adhesion molecules. This phenomenon correlates with the increased number of adhesion bonds, which rises to approximately 40 in high-shear regions, compared to around 12 for straight vessels and approximately 5-6 in low-shear regions. The findings also indicate an optimal cellular stiffness necessary for successful CTC extravasation in curved vessels. Discussion: By the quantitative assessment of the risk of CTC extravasation as a function of vessel tortuosity, our study offers a novel tool for the prediction of metastasis risk to support the development of personalized therapeutic interventions based on individual vascular characteristics and tumor cell properties.

Minimization of metabolic cost of transport predicts changes in gait mechanics over a range of ankle-foot orthosis stiffnesses in individuals with bilateral plantar flexor weakness

Neuromuscular disorders often lead to ankle plantar flexor muscle weakness, which impairs ankle push-off power and forward propulsion during gait. To improve walking speed and reduce metabolic cost of transport (mCoT), patients with plantar flexor weakness are provided dorsal-leaf spring ankle-foot orthoses (AFOs). It is widely believed that mCoT during gait depends on the AFO stiffness and an optimal AFO stiffness that minimizes mCoT exists. The biomechanics behind why and how an optimal stiffness exists and benefits individuals with plantar flexor weakness are not well understood. We hypothesized that the AFO would reduce the required support moment and, hence, metabolic cost contributions of the ankle plantar flexor and knee extensor muscles during stance, and reduce hip flexor metabolic cost to initiate swing. To test these hypotheses, we generated neuromusculoskeletal simulations to represent gait of an individual with bilateral plantar flexor weakness wearing an AFO with varying stiffness. Predictions were based on the objective of minimizing mCoT, loading rates at impact and head accelerations at each stiffness level, and the motor patterns were determined via dynamic optimization. The predictive gait simulation results were compared to experimental data from subjects with bilateral plantar flexor weakness walking with varying AFO stiffness. Our simulations demonstrated that reductions in mCoT with increasing stiffness were attributed to reductions in quadriceps metabolic cost during midstance. Increases in mCoT above optimum stiffness were attributed to the increasing metabolic cost of both hip flexor and hamstrings muscles. The insights gained from our predictive gait simulations could inform clinicians on the prescription of personalized AFOs. With further model individualization, simulations based on mCoT minimization may sufficiently predict adaptations to an AFO in individuals with plantar flexor weakness.

Dynamic analysis of drag-based vibratory swimmers using higher-order averaging

This paper discusses the mathematical modeling, dynamic analysis, and design optimization of a class of drag-based vibratory swimmers using averaging. A typical swimmer of this class consists of a surface or subsurface main body, an oscillatory mass inside the body, and a rigid fin attached to the main body using torsional springs and immersed in water. This paper takes advantage of third-order averaging techniques for dynamic analysis and design optimization of the swimmer for high frequencies. The averaged dynamics are used for determining the optimum stiffness of the springs for maximizing the average speed of the swimmer for high-frequency motion of the oscillatory mass. Experimental results confirm the general response of the mathematical model.

Static and dynamic stiffness optimization on the body structure of an electric quadricycle

Reducing vehicle vibrations is of particular importance due to the adverse effect of vibrations on the ride comfort of passengers. Electric quadricycles are growing rapidly because they are quieter and less polluting than fossil-fuelled vehicles, and these reasons make them a green alternative to personal transportation, and their popularity increases day by day. In this article, the optimization of the body structure of EQ10, an electric quadricycle under development, is discussed to reduce the weight and vibrations transmitted to the passengers with the constraints of bending stiffness and torsional stiffness and yield stress of the elements. The vibrations transmitted to the occupants are measured beneath the driver’s seat by reading the acceleration resulting from the EQ10 excitation sources vibrations. First, a finite element model of the body structure was designed. Then, for optimization, the EQ10 body structure is divided into 29 modules, and in the optimization process, the thickness of these 29 modules is considered as a design variable. The BIGOPT gradient-based method was chosen to solve the optimization problem due to its superior performance to other numerical solution algorithms. To calculate static and dynamic stiffness, modal analyses, and frequency transfer function are conducted to evaluate its general behavior under various functional conditions. Following optimization, results show that the bending and torsional stiffness increased by 45% and 31%, respectively; such fascinating results could not have been obtained without the methods employed in this investigation.

Changes in gastrocnemius MTU stiffness and their correlation with plantar pressure in patients with knee osteoarthritis.

Abnormal, excessive, and repetitive knee load is a critical risk factor for osteoarthritis (OA). The gastrocnemius muscle-tendon unit (MTU) interacts with foot biomechanics and is vital in cushioning the knee load. Abnormal gastrocnemius activation and plantar pressure during walking in patients with knee OA may negatively affect gastrocnemius MTU stiffness, increasing knee load. Few studies investigated the relationship between gastrocnemius MTU stiffness and plantar pressure. This study aimed to evaluate the changes in gastrocnemius MTU stiffness in patients with knee OA and their correlations with plantar pressure and clinical symptoms. Thirty women patients with unilateral knee OA and 30 healthy women participants were recruited. Shear wave elastography was used to quantify gastrocnemius MTU stiffness in ankle resting and anatomical 0° positions, defined as natural and neutral positions in this study. A plantar pressure analysis system was used to collect the plantar pressure parameters on the symptomatic side in patients with knee OA. The Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC) and Visual Analogue Scale (VAS) scores were used to measure the severity of clinical symptoms. Medial and lateral gastrocnemius (MG and LG) stiffness on both the asymptomatic and symptomatic sides in patients with knee OA was increased compared with that in healthy participants. The MG and LG optimal cutoff stiffness in the natural position was 15.73kPa and 14.25kPa, respectively. The optimal cutoff stiffness in the neutral position was 36.32kPa and 25.43kPa, respectively, with excellent sensitivity and specificity. The MG and LG stiffness were positively correlated with the percentages of anterior and medial plantar pressure and negatively correlated with the length of pressure center path. The LG and MG were significantly correlated with WOMAC and VAS scores. Patients with knee OA have increased gastrocnemius muscle stiffness, closely related to plantar pressure and clinical symptoms. Monitoring the gastrocnemius muscle in patients with knee OA can provide an essential basis for its prevention and treatment.

Stability analysis of multi-insert rotating boring bar with stiffness variation

Manufacturing faces challenges in boring processes, critical for hole enlargement and finishing, due to low stiffness leading to static deflection and regenerative chatter. Stiffness variation has emerged as a promising solution for effectively suppressing chatter, while multi-insert rotating boring bars offer a viable approach to addressing static deflection in long and slender boring bars, enabling better tolerance with a large operational length-to-diameter ratio. However, integrating technological innovations to suppress chatter and prevent static deflection complicates the problem from a modeling and stability analysis perspective, making it challenging to find a comprehensive solution in the existing literature. This study explores the stability of multi-insert rotating boring bars with stiffness variation, providing insights into selecting optimal stiffness variation parameters. It introduces a novel extension of the multi-dimensional cutting force model to rotating boring tools with multiple inserts, employing the zero-order harmonic solution to analyze the stability of boring processes with time-varying dynamics. Experimental validation demonstrates the effectiveness of the proposed methodology, achieving 5 out of 6 matches in stability lobe diagrams for multi-insert rotating boring bars without stiffness variation. The model’s comprehensiveness is further demonstrated by comparing the results with those of existing studies in the literature for single-insert stationary boring bars. In the case without stiffness variation, the model successfully reproduces 4 out of 5 operating points, and with stiffness variation, it accurately predicts all 5 operating points. Sensitivity analyses guide the selection of optimal stiffness variation parameters for effective chatter suppression, favoring moderate frequencies and up to a 30% amplitude ratio.

Stretchable rubber composites with lower hysteresis losses, improved magnetic effect, and a robust magnetic sensitivity

The stretchable materials exhibit various challenges such as high hysteresis losses, lower magnetic effect, and less magnetic sensitivity. In this work, we design and fabricate stretchable magnetic-rheological elastomers based on silicone rubber with robust magnetic sensitivity and lower hysteresis losses. The nanofillers used were carbon black (CB), and electrolyte iron particle (EIP). The stretchable materials obtained show an anisotropic effect of up to 165%. Moreover, the hysteresis losses were 0.4 kJ (control), 2.45 kJ (15 phr of CB), 0.58 kJ (60 phr of EIP), and 3.53 kJ (60 phr of hybrid filler system). The compressive modulus was 1.4 MPa (control), 3.76 MPa (15 phr of CB), 2.1 MPa (60 phr of EIP), and 3.9 MPa (60 phr of hybrid filler system). The fracture strain was 164% (control), 160% (15 phr of CB), 100% (60 phr of EIP), and 139% (60 phr of hybrid filler system). To sum up, the CB shows robust mechanical properties with high stretchability. However, the hybrid filler system shows high stiffness with a higher magnetic response. Finally, EIP-filled composites show optimum stiffness and robust magnetic response force.

Study of backflow volume due to check valve’s lag motion in liquid hydrogen piston pump

The liquid hydrogen piston pump is the key equipment in the process of storage, transportation, and refueling of liquid hydrogen. The timely motions of suction and discharge valves are beneficial to the transport performance and volumetric efficiency of the pump. This study sets up an operation frame of the liquid hydrogen piston pump in which reciprocating pistons and check valves with a conical spool interact. Backflow occurs when there is a delay in the spool’s motion, which is more common in suction valves than in discharge valves. The influence of spring stiffness and spool-head angle of the valve cone on the suction valve’s backflow volume is analyzed and further optimized. The results indicate that there exists an optimal spool-head angle and spring stiffness for minimizing backflow volume during the closing phase of the suction valve. This research contributes to enhancing the volumetric efficiency of the liquid hydrogen piston pump.

Bowstring-type inerter negative stiffness damper for vibration control of slender towers

The difficulty of practical installation restrains the application of tuned damping devices in the high-performance vibration control of slender towers. In order to address this issue, a novel Bowstring-type Inerter Negative Stiffness Damper (BINSD) is proposed. The BINSD is composed of an inerter-negative-stiffness-dashpot system connected between the tower and a mass block (or a massless node) located on a vertical prestressed cable like a bowstring. In order to determine the multiple optimal parameters of the proposed BINSD, analytical parametric optimizations are investigated for the following three aspects. Firstly, the optimal tuning frequency and damping ratios are obtained via an analytical approach considering H∞ and H2 norms. Secondly, the optimal negative stiffness is determined by balancing the static and dynamic performances, particularly for practical excitations with mixed static and dynamic components (such as wind). Thirdly, the optimal installation height is analytically derived to fulfil a least negative stiffness criterion, which leads to an economic realization in practice. Finally, the effectiveness of the presented BINSD and corresponding optimal design approaches is numerically validated by the wind- and seismic- induced vibration control cases of a wind turbine tower. The proposed optimal design approaches lead to a high-performance, economic, and feasible design of BINSD.

Free vibration analysis of hybrid CNT/GPL-reinforced Porous composite plates under fluid-loading

The present study aims to explore free vibration analysis of hybrid reinforced porous composite plates subjected to fluid loading. The hybrid composite comprises a porous core layer covered by two reinforced porous face sheets. Graphene Platelets (GPLs) and Carbon Nanotubes (CNTs) are considered as reinforcement materials. The linear three-dimensional piezo-elasticity theory is employed to model the structural part of the system, while the classical Rayleigh integral is used to obtain the fluid interaction part. The accuracy and reliability of the proposed model are validated by comparing the calculated natural frequencies of the plate in vacuum and water-loaded conditions with those reported in the literature. For the first time, several parametric studies are performed to investigate the effects of dimension ratios, porosity distributions, reinforcement dispersion pattern, porosity coefficient, and weight fraction of nanofiller on the natural frequency of hybrid reinforced porous composites. The results indicate that adjusting the porosity and weight fraction of the face sheets can enhance stiffness without changing the mass, emphasizing the importance of hybrid composites for achieving optimal stiffness while maintaining a constant mass. Furthermore, the influence of core layer porosity distributions on the composite behavior differs from that of porosity distributions in the face layers. Additionally, the effectiveness of the reinforcement pattern depends on the type of porosity distribution in the face layers.