Stiff Frame Research Articles

In-plan distribution of peak floor acceleration demands in torsionally irregular buildings

The precise estimation of peak floor acceleration demands is essential to ensure the seismic safety of building contents and attachments. The present study aims to investigate the distribution of the peak floor acceleration demands across the floor plan in torsionally irregular buildings. To achieve this objective, 28 mid-rise reinforced concrete buildings with torsional irregularities are analyzed under 5600 bidirectional earthquake excitations, considering various strength ratios in buildings. A total of 2,59,200 in-structure amplification factors are estimated at multiple locations within the building plan and also at different floors. It is observed that current seismic design codes tend to underestimate the in-structure amplification factor for torsionally irregular buildings, particularly at locations distant from the center of rigidity (towards flexible frames), by up to 137 % for elastic buildings, and up to 54 % for moderately inelastic buildings. Even in the case of frames closer to the stiff frames, the seismic design codes underestimated the in-structure amplification factor by up to 68 % for elastic buildings. It is observed that a strong relationship exists between the torsional amplification of the peak floor acceleration and displacement amplification due to building torsion at the floor of interest. The torsional amplification of peak floor acceleration is found to be approximately equal to torsional displacement amplification for the flexible frames at the floor of interest. Simplified equations are developed for their integration with existing building codes to precisely estimate the in-plan distribution of peak floor acceleration demands in torsionally irregular buildings.

Influence of Active-to-Passive Ratio on the Deformation in Circular Dielectric Elastomer Actuators.

To further improve the performance of dielectric elastomer actuaotrs (DEAs), the development of novel elastomers with enhanced electro-mechanical properties is focal for the advancement of the technology. Hence, reliable techniques to assess their electro-mechanical performance are necessary. Characterization of the actuator materials is often achieved by fabricating circular DEAs with the pre-stretch of the membrane fixed by a stiff frame. Because of this set-up, the electrode size relative to the carrier frame's dimension has an impact on actuator strain and displacement. To allow for comparable results across different studies, the influence of this effect needs to be quantified and taken into account. This paper presents an in-depth study of the active-to-passive ratio by proposing two simplified analytical models for circular DEA and comparing them. The first model is taking the hyperelastic material properties of the dielectric film into account while the second model is a linear elastic lumped parameter model based on the electro-mechanical analogy. Both models lie in good agreement and show a significant linear impact of the radial active-to-passive ratio on the electro-active strain and a resulting maximum of displacement around 50% radial coverage ratio. These findings are validated by experiments with actuators fabricated using silicone membranes. It is shown that the electrode size is not only an important parameter in the experimental design, but in some cases of higher significance for the accuracy of analytical models than the hyperelastic properties of the material. Furthermore, it could be shown that a radial coverage ratio of around 50% is desirable when measuring displacement as it maximizes the displacement and lowers the impact of deviations in electrode sizes due to fabrication errors.

Understanding the Impact of Active-to-Passive Area Ratio on Deformation in One-Dimensional Dielectric Elastomer Actuators with Uniaxial Strain State.

There is increasing interest in the use of novel elastomers with inherent or modified advanced dielectric and mechanical properties, as components of dielectric elastomer actuators (DEA). This requires corresponding techniques to assess their electro-mechanical performance. A common way to test dielectric materials is the fabrication of actuators with pre-stretch fixed by a stiff frame. This results in the problem that the electrode size has an influence on the achievable actuator displacement and strain, which is detrimental to the comparability of experiments. This paper presents an in-depth study of the active-to-passive ratio with the aim of investigating the influence of the coverage ratio on uniaxial actuator displacement and strain. To model the effect, a simple lumped-parameter model is proposed. The model shows that the coverage ratio for maximal displacement is 50%. To validate the model results, experiments are carried out. For this, a rectangular, fiber-reinforced DEA is used to assess the relation of the coverage ratio and deformation. Due to the stiffness of the fibers, highly anisotropic mechanical properties are achieved, leading to the uniaxial strain behavior of the actuator, which allows the validation of the one-dimensional model. To consider the influence of the simplifications in the lumped-parameter model, the results are compared to a hyperelastic model. In summary, it is shown that the ratio of the active-to-passive area has a significant influence on the actuator deformation. Both the model and experiments confirm that an active-to-passive ratio of 50% is particularly advantageous in most cases.

Cosmic Ray Detector Using Geiger Tubes and Coincident Pulses

Cosmic Rays (CRs) are extreme strength particles resigning from outside the Earth and transported through space. These atoms can considerably impact human fitness, aviation and photo electric suppliers. A high energy radiation from space indicator is a tool that detects and measures the force of limitless beams. In this project, one can build a high energy radiation from space indicator utilizing two Geiger Muller tubes, Lead sheets, a stiff frame, a Microcontroller and a Protractor to regulate the frame at certain angle. At different altitudes, at different temperatures, at different humidities, we can identify and record CRs. A portable Muon Detector project that incorporates two Geiger Tubes enclosed within a lead sheet for detecting CRs. The system utilizes a coincidence circuit login to enhance the detection accuracy and reduce false positive rates. Additionally, the device is equipped with sensors to collect data on Temperature, Humidity, Latitude, Longitude and Atmospheric Pressure. The combination of these features provides a comprehensive and versatile solution for studying Muons and their interactions with the surrounding environment.

Hydrostatic, strike-slip and normal stress true triaxial hydrofracturing testing of Blanco Mera Granite: breakdown pressure and tensile strength assessment

We have designed and built a versatile testing device to perform hydraulic fracturing experiments under true triaxial conditions. The device, based on a stiff biaxial frame that can be installed in a servocontrolled press, can accommodate cube rock samples of up to 150 mm-edge. Using a low-permeability rock known as Blanco Mera granite, we have performed a series of tests across a range of confining pressures including hydrostatic, normal, and strike-slip regimes. We have verified the applicability of two simple fracture mechanics-based models for the interpretation of experimental results, and we have determined the value of tensile strength of the rock from the injection curves recorded. The orientation of the hydraulically-triggered fractures with respect to the applied stress has also been analyzed. Although the models proposed by Rummel and Abou-Sayed provided reasonably satisfactory results, especially for hydrostatic and strike-slip tests, the presence of heterogeneities and defects in the rock matrix may have a strong influence on the fracture behavior and, therefore, affect the interpretation of hydrofracturing tests.

A soft thumb-sized vision-based sensor with accurate all-round force perception

Vision-based haptic sensors have emerged as a promising approach to robotic touch due to affordable high-resolution cameras and successful computer vision techniques; however, their physical design and the information they provide do not yet meet the requirements of real applications. We present a robust, soft, low-cost, vision-based, thumb-sized three-dimensional haptic sensor named Insight, which continually provides a directional force-distribution map over its entire conical sensing surface. Constructed around an internal monocular camera, the sensor has only a single layer of elastomer over-moulded on a stiff frame to guarantee sensitivity, robustness and soft contact. Furthermore, Insight uniquely combines photometric stereo and structured light using a collimator to detect the three-dimensional deformation of its easily replaceable flexible outer shell. The force information is inferred by a deep neural network that maps images to the spatial distribution of three-dimensional contact force (normal and shear). Insight has an overall spatial resolution of 0.4 mm, a force magnitude accuracy of around 0.03 N and a force direction accuracy of around five degrees over a range of 0.03–2 N for numerous distinct contacts with varying contact area. The presented hardware and software design concepts can be transferred to a wide variety of robot parts.

Hydrofracturing tests on granite samples using a true triaxial device equipped with acoustic emission sensors

We present a series of tests performed on granite samples using a true triaxial device designed and built at the Rock Mechanics Laboratory (University of A Coruña). The experiments were performed using cubic rock samples of 150 mm-edge, which were loaded to different stress conditions (σh < σh < σy < 45 MPa) on each loading axis. The device is based on a stiff steel frame that can be coupled to a servo-hydraulic testing machine that provides de vertical stress (av), while two high-pressure pumps are used to deliver the lateral stress (σh and ah). An additional high-pressure pump is used to inject the fluid (mineral oil) into the rock sample at a low constant-flow rate. The aluminium loading platens, which are bevelled at the edges to avoid interaction among adjacent faces, have holes and grooves to introduce acoustic emission sensors that allow the location of fracture propagation. The specimens were drilled using a 6 mm drill bit until reaching the geometrical centre. Then, a 1/8” (~3.18 mm) stainless steel tube is glued to the samples with epoxy. Strain measurements during the experiments were conducted using four strain gages attached to the orthogonal faces of the specimens. The system was further equipped with three LVDTs to account for the bulk displacement on each axis. Our results suggest a linear relationship between the breakdown pressure and the confining stress under hydrostatic conditions but no clear correlation in non-hydrostatic stress regime.

Simultaneous shape and topology optimization method for frame structures with multi-materials

In this study, we present a novel non-parametric shape-topology optimization method for frame structures with multi-materials, aiming at designing more light and stiff frame structures. The sum of squared error norm for achieving the target displacements on the specified members is minimized under the volume constraints of multi-materials as a design problem. A simultaneous shape and topology optimization problem is formulated as a distributed-parameter optimization problem based on the variational method. The shape gradient function and the material gradient functions for this design optimization problem are theoretically derived with the Lagrange multiplier method, the material derivative method and the adjoint variable method. The generalized solid isotropic material with penalization (GSIMP) method is employed to classify into the multi-materials in topology optimization. The gradient functions derived are applied to the unified H1 gradient method for frame structures to determine the optimal shape and material variations. With this method, the optimal free-form and topology for arbitrary large-degree of design freedom frame structures with multi-materials can be obtained without any shape and topology parameterization. Numerical examples with various materials and different boundary conditions are demonstrated and the results are discussed.

Elastic-plastic time-history analysis of steel-tube stiff-frame arch bridge without inner filling concrete

Based on a case study of a typical arch bridge with hollow steel tube and stiffness frame located in the high intensity region of western China, this paper adopts the onlinear time- history method to analyze the structural response of the overall bridge elastic-plastic model under seismic action. Under the force of Wolong wave in Wenchuan Earthquake, the main load-bearing members of the structure have a good seismic performance. Only part of the columns on the main arch ring enter the plastic hinge state for energy dissipation, and the lower columns have a more obvious energy dissipation effect than the higher ones. The result indicates that the design idea of structure which is similar to that of strong column and weak beam in ductility design, has the characteristics of “strong arch and weak beam” and can therefore improve the ability of structure to resist collapse under earthquake action.

Evaluation of seismic torsional response of ductile RC buildings with soft first story

This study investigates the inelastic torsional response of plan asymmetric ductile RC buildings with a soft first story. The buildings of Rectangular, L, T, and U plan shapes are considered for the study. Force-based fiber beam-column elements are modeled for the inelastic response prediction of the buildings. Masonry infill walls are uniformly distributed in the plan and considered for the evaluation of torsional response. The pushover methods, Extended N2 and Extended Capacity Spectrum Method – FEMA 440 are adopted to estimate the inelastic torsional response. Bi-directional nonlinear time history analysis is carried out on the buildings considering near-field and far-field ground motions. Story drift ratio and curvature demand-capacity (D/C) ratio of columns are reported at the stiff, flexible side of buildings. The torsional response of infill wall buildings is compared with that of bare frame buildings. It was observed that the torsionally irregular ductile buildings with soft first story exhibit higher seismic demand on the flexible side corner columns. Infill wall interaction amplifies the torsional response at the bottom story, causing an increase in displacements higher at the flexible side and moderate near the stiff side. This study concludes that the flexible side corner column in plan asymmetric building with a soft first story can be conservatively designed for 1.5 times the design forces obtained from the analysis. This conservative design ensures stable energy dissipation in the corner column under load reversals, without significant strength reduction under higher excitation levels. The designer shall properly distribute lateral load resisting elements in a plan to prevent premature failure of the columns located internally and close to the initial center of rigidity. The designer can avoid the collapse of columns located internally in the buildings with stiff peripheral frames by designing for forces 1.5 times higher than obtained.

Edge-clamped two-way slabs containing low-ductility steel

This paper describes a series of full range load tests on two-way, edge-clamped reinforced concrete slab panels containing either Class L WWF or Class N deformed bars. Five rectangular slab panels were tested each with two adjacent fully restrained edges and two free edges. A point support was included under the corner of each panel at the intersection of the two free edges. Each slab specimen was loaded by four transverse loads applied symmetrically in the mid-panel region by a deformation-controlled actuator in a stiff testing frame. The continuous edge supports were provided by clamping two adjacent edges in a carefully designed and constructed testing frame. The slabs were instrumented with load cells to measure applied forces and reactions, strain gauges to measure strain in the steel reinforcement and on the concrete surfaces, linear variable displacement transducers and lasers to measure deflections at all stages of loading. The results of the tests are presented and evaluated, with particular emphasis on the strength, ductility and failure mode of the slabs.

Shake-Table Seismic Performance Evaluation of Direct- and Indirect-Hung Suspended Ceiling Systems

ABSTRACT Suspended ceiling systems are among the most frequently reported earthquake-vulnerable nonstructural elements. Despite their importance, a rational seismic design procedure for suspended ceiling systems has not been developed because of their complex details and behavior. In this study, the seismic performance of direct- and indirect-hung suspended ceilings was evaluated based on shake table tests. In particular, a large-size ceiling specimen, comparable to an actual constructed size, was tested using an array of two shake tables and a highly stiff test frame with overall dimensions of 13 (length) × 5 (width) × 3 (height) m. In addition, six smaller specimens were tested using one shake table. All the specimens were prepared as free-floating systems by permitting free movements at the four edges. Based on the test results, key engineering parameters related to acceleration amplification and natural frequency were identified and the overall seismic performance was evaluated. Compared with the extensive failure observed in the lay-in panel ceiling specimens, marginal damage occurred around the pounded edge in the continuous panel ceiling specimens because of the robust restraining effects of the screw-attached panels on the ceiling grid members. The median amplification factors observed in the tested suspended ceiling specimens were about 1.80 and 1.75 for the vertical and horizontal directions, respectively. The dynamic behavior of the tested indirect-hung suspended ceilings which used long hanger bolts was significantly different from the pendulum behavior observed in the direct-hung suspended ceilings. The unidirectional rotation-restraining characteristic of the hanger bolt connection imparted different behaviors in each orthogonal direction. The natural frequencies of the tested suspended ceilings were well predicted when the deformed shape of the hanger bolt was modeled as a single curvature bending in the rotation-free direction and a double curvature bending in the rotation-restrained direction. The damage evaluation of each ceiling system was also presented through incremental-intensity shake table testing.

Torsional ductility spectrum for predicting ductility distribution in simple asymmetric‐plan structures

SummaryAn analytical procedure is developed for predicting the ductility demands in simple asymmetric‐plan structures under earthquake ground motions. The procedure governs regular structures dominated by the lower vibration modes where inelastic response occurs only at the bases of first story columns and at the beam ends, in conformance with the capacity design principles. Torsional ductility spectra are generated for expressing the maximum ductility response of torsionally coupled, generic, single‐story, 2‐degree‐of‐freedom inelastic parametric systems. Five parameters characterize the parametric systems: first mode period, uncoupled frequency ratio, stiffness eccentricity, stiff‐to‐flexible edge strength ratio, and ductility reduction factor. A surrogate modeling approach is developed for converting the properties of the actual systems to those of the parametric system. Mean maximum ductilities of torsionally stiff, equally stiff, and torsionally flexible systems are calculated under a set of design spectrum compatible strong motions for the possible combinations of characteristic parameters. The results obtained from case studies revealed reasonable accuracy of the estimations. The results have indicated that the flexible side frames of torsionally stiff and equally stiff code conforming designs are mainly responsible for providing the intended ductility and energy dissipation capacity whereas the stiff side frames play a secondary role, particularly when the stiff edge is significantly stronger than the flexible edge. However, ductility demands in torsionally flexible systems are significantly larger at both sides compared with torsionally stiff systems.

Kirigami-Design-Enabled Hydrogel Multimorphs with Application as a Multistate Switch.

Morphing materials have promising applications in soft robots, intelligent devices, and so forth. Among the various design strategies, kirigami structures are recognized as a powerful tool to obtain sophisticated 3D configurations and unprecedented properties from planar designs on common materials. Here, some kirigami designs are demonstrated for programmable, multistable 3D configurations from composite hydrogel sheets. Via photolithographic polymerization, perforated composite hydrogel sheets are fabricated, in which soft and active hydrogel strips are patterned in stiff and passive hydrogel frames. When immersed in water, the gel strips buckle out of plane due to swelling mismatch. In the kirigami structures, the geometric continuity is disrupted by the introduction of cutouts, and thus the degrees of deformation freedom increases remarkably. Multiple configurations are obtained in a single composite hydrogel by controlling the buckling direction of each strip. Multitier configurations are also obtained by using a hierarchically designed kirigami structure. A multicontact switch of an electric circuit is designed by harnessing the multitier gel configurations. Furthermore, a rotation mode is realized by introducing chirality in the kirigami design. The versatile design of the kirigami structure for programmable deformations should be applicable for other intelligent materials toward promising applications in biomedical devices and flexible electronics.

Development of a Functional 3D Bioprinted Vascular Smooth Muscle Tissue Model Using a Stiffness‐Modifiable Alginate‐Collagen‐Fibrinogen Based Bioink

BackgroundBlood vessels are soft tissues whose cellular functions are regulated in part by mechanical signals from the extracellular matrix. Structural defects including increased vascular wall stiffness are known contributors to the initiation and progression of diseases like pulmonary hypertension and atherosclerosis. However, studying the effects of wall stiffness using traditional 2 dimensional (2D) cell culture models pose challenges: the flat plastic surface is very stiff and incapable of accurately replicating altered tissue structure. Using 3D bioprinting technology and a stiffness‐modifiable alginate‐collagen‐fibrinogen bioink, we aimed to fabricate functional tissue mimicking the medial smooth muscle layer of healthy and diseased blood vessels.MethodsPulmonary and coronary arterial smooth muscle cells (PASM and CASM respectively) were encapsulated at 2.5x107 cells/mL in a bioink comprised of 0.25% to 1.0% w/v sodium alginate, 1 mg/mL collagen‐I, and 5 mg/mL fibrinogen. Tissues were bioprinted with an Aspect Biosystems RX‐1 bioprinter as an 8–10 mm ring, free‐floating or constrained within a stiff (0.75–1.25% alginate) acellular load bearing frame, then treated with thrombin (1.25 U/mL, 30 min) for fibrin polymerisation. To assess tissue integrity and function, tissue compaction was assessed by reduction of lumen area and cell organization was determined using filamentous actin staining.ResultsStiff (1% alginate) PASM biorings without a frame were mechanically stable, but cells remained ‘balled up’ and were unable to spread within the structure. Softer (0.25% and 0.5% alginate) PASM biorings showed signs of cell spreading but exhibited excessive compaction (&gt;70% lumen area reduction) within 24 hours. Addition of a 1% alginate frame to PASM biorings reduced compaction to 6.94% (0.25% cellular alginate) and 3.69% (0.5% cellular alginate), while still allowing cells to elongate and form cell‐cell networks. Similar results were observed with CASM biorings, which compacted &gt;50% when printed without a frame. We demonstrated that the degree of tissue compaction is controllable using frames of different stiffnesses; soft (0.375% alginate) CASM biorings printed with a 0.75% alginate frame had &gt;15% compaction, whereas biorings with stiffer 1% and 1.25% alginate frames exhibited &lt;5% compaction. In all cases, cells printed in soft biorings with stiff frames had well‐organised bundles of actin filaments consistent with real vascular smooth muscle.ConclusionOur stiffness‐modifiable 3D bioprinted smooth muscle represents a novel experimental model for studying vascular tissue. The bioink composition and physical design, where muscle compaction can be easily controlled by altering the acellular load bearing frame, allows us to better mimic the structural defects seen in vascular diseases than is possible with 2D models. This makes our model a powerful tool that will enable us to understand how wall stiffness affects the initiation and progression of vascular diseases.Support or Funding InformationNSERC Discovery Grant (ARW), Research Manitoba Studentship (SS, JO), CHRIM Operating Grant

Smart Seismic Control System for High-Rise Buildings Using Large-Stroke Viscous Dampers Through Connection to Strong-Back Core Frame

An innovative structural control system is proposed for high-rise buildings. A damping layer is provided between a stiff upper core frame suspended from the top of the main building and a stiff lower core frame connected to the building foundation. As the ratio of stiffness of both core frames to that of the main building becomes larger, the relative displacement in the damping layer (damper deformation) approaches to the top floor displacement of the main building. The large displacement of the top floor displacement of the main building is taken full advantage in the proposed control system as most of the total displacement of the main building results from the damper deformation instead of interstory drift. Transformation of the multi-degree-of-freedom (MDOF) model into the single-degree-of-freedom (SDOF) model enables a simplified but rather accurate response evaluation for pulse-type and long-duration earthquake ground motions. The results of the time history response analysis of buildings including this control system are presented for various recorded ground motions. Finally, the effectiveness of the proposed structural control system is discussed from the viewpoint of earthquake input energy.

Seismic Assessment of Footbridges under Spatial Variation of Earthquake Ground Motion (SVEGM): Experimental Testing and Finite Element Analyses.

In this paper, the seismic assessments of two footbridges, i.e., a single-span steel frame footbridge and a three-span cable-stayed structure, to the spatial variation of earthquake ground motion (SVEGM) are presented. A model of nonuniform kinematic excitation was used for the dynamic analyses of the footbridges. The influence of SVEGM on the dynamic performance of structures was assessed on both experimental and numerical ways. The comprehensive tests were planned and carried out on both structures. The investigation was divided into two parts: in situ experiment and numerical analyses. The first experimental part served for the validation of both the finite element (FE) modal models of structures and the theoretical model of nonuniform excitation as well as the appropriateness of the FE procedures used for dynamic analyses. First, the modal properties were validated. The differences between the numerical and the experimental natural frequencies, obtained using the operational modal analysis, were less than 10%. The comparison of the experimental and numerical mode shapes also proved a good agreement since the modal assurance criterion values were satisfactory for both structures. Secondly, nonuniform kinematic excitation was experimentally imposed using vibroseis tests. The apparent wave velocities, evaluated from the cross-correlation functions of the acceleration-time histories registered at two consecutive structures supports, equaled 203 and 214 m/s for both structures, respectively. Also, the coherence functions proved the similarity of the signals, especially for the frequency range 5 to 15 Hz. Then, artificial kinematic excitation was generated on the basis of the adopted model of nonuniform excitation. The obtained power spectral density functions of acceleration-time histories registered at all supports as well as the cross-spectral density functions between registered and artificial acceleration-time histories confirmed the strong similarity of the measured and artificial signals. Finally, the experimental and numerical assessments of the footbridges performance under the known dynamic excitation generated by the vibroseis were carried out. The FE models and procedures were positively validated by linking full-scale tests and numerical calculations. In the numerical part of the research, seismic analyses of the footbridges were conducted. The dynamic responses of structures to a representative seismic shock were calculated. Both the uniform and nonuniform models of excitation were applied to demonstrate and quantify the influence of SVEGM on the seismic assessment of footbridges. It occurred that SVEGM may generate non-conservative results in comparison with classic uniform seismic excitation. For the stiff steel frame footbridge the maximum dynamic response was obtained for the model of nonuniform excitation with the lowest wave velocity. Especially zones located closely to stiff frame nodes were significantly more disturbed. For the flexible cable-stayed footbridge, in case of nonuniform excitation, the dynamic response was enhanced only at the points located in the extreme spans and in the midspan closely to the pillars.

Monotonic shear strength of headed studs in reinforced infill walls

Headed studs are key components of structures which facilitate composite behavior between steel and concrete elements. In steel building structures, reinforced concrete infill walls surrounded by a stiff steel frame is a common example of a composite structure used to resist horizontal loads such as those produced by earthquakes or wind. To this end, these types of concrete walls need to be anchored to the steel frame with headed studs which must withstand shear and tensile forces (AISC 360). To properly design headed stud anchors in concrete walls, it is first necessary to understand their behavior when subjected to monotonic shear forces considering edge conditions and reinforcing details that may influence the stud strength.Few tests have examined headed studs subjected to monotonic shear with typical boundary effects in reinforced infill walls, so a new experimental study on 17 specimens explores the behavior of headed studs exposed to monotonic shear loading with group effects. The experiments showed that the strength of studs installed in infill walls with edge conditions is well predicted (average error in prediction is smaller than 10%) by ACI 318, AISC 360 and EC-4. However, when group effects of anchors are included in the analysis of infill walls, only the ACI 318 is able to predict the behavior.

Design Optimisation of Acoustic Absorbers with Cross-Like Pores Via a Homogenisation Method

Mechanical modelling and associated numerical methods are able to improve the design of absorbing materials which are otherwise difficult to accomplish through experimental studies only. In this paper, we provide an original procedure for obtaining high acoustic absorption of single and multi-layered panels with predefined microstructure. The procedure uses the homogenisation technique for obtaining effective properties of an airsaturated material and solution to acoustic problems. We study a certain topology of the material and point out the effect of matrix material stiffness on the results of the optimisation procedure. We demonstrate that for stiff and rigid frames of a single layer, the optimal design parameters do not differ much whereas for the soft frames, the same results may significantly change. Moreover, we show that the absorption properties can be essentially improved by arrangements of different materials (soft, stiff and air) in sandwich panels. It is also possible to design a material which efficiently absorbs acoustic energy at low frequencies which is hard to achieve by means of conventional materials.

Simple stress–strain model of very strong limestones and dolomites for engineering practice

This paper presents a simple mathematical model that can be used in engineering practice to estimate the stress–strain behavior of very strong limestones and dolomites (σc > 100 MPa) subjected to uniaxial compression. This model is developed using the canonical form of Haldane’s distribution function. To estimate the stress–strain response using the proposed model, sophisticated stiff load frames are not needed. It is argued that only a simple uniaxial tester (with a hand pump) for one point measurement at a small stress and Schmidt hammer are required to estimate stress–strain response from zero strain/zero stress up to failure.